Daily Papers

Longitudinal chest X-ray (CXR) interpretation requires reasoning over disease evolution across multiple patient visits, yet most existing medical VQA benchmarks focus on single images or short-horizon image pairs. We introduce MI-CXR, a benchmark for standardized evaluation of Multi-Interval longitudinal reasoning over multi-visit CXR sequences, without requiring free-form report generation or additional clinical context. MI-CXR comprises five-way multiple-choice questions over five-visit patient timelines and instantiates three complementary task families: Temporal Event Localization, Interval-wise Change Reasoning, and Global Trajectory Summarization, which assess clinically grounded visual reasoning over time. Evaluating 14 state-of-the-art vision-language models (VLMs) shows low overall performance, with an average accuracy of 29.3%, only modestly above random guessing. Using stage-wise diagnostic probing, we find that models often produce locally plausible interval descriptions but fail to enforce temporal constraints or compose evidence into globally consistent decisions over the full timeline. These findings reveal key limitations of current VLMs and establish MI-CXR as a principled benchmark for longitudinal medical reasoning. The benchmark is available at https://github.com/AIDASLab/MI-CXR

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

To enable Large Language Models (LLMs) to function as conscious agents with generalizable reasoning capabilities, it is crucial that they possess the reasoning ability to comprehend situational changes (transitions) in distribution triggered by environmental factors or actions from other agents. Despite its fundamental significance, this ability remains underexplored due to the complexity of modeling infinite possible changes in an event and their associated distributions, coupled with the lack of benchmark data with situational transitions. Addressing these gaps, we propose a novel formulation of reasoning with distributional changes as a three-step discriminative process, termed as MetAphysical ReaSoning. We then introduce the first-ever benchmark, MARS, comprising three tasks corresponding to each step. These tasks systematically assess LLMs' capabilities in reasoning the plausibility of (i) changes in actions, (ii) states caused by changed actions, and (iii) situational transitions driven by changes in action. Extensive evaluations with 20 (L)LMs of varying sizes and methods indicate that all three tasks in this process pose significant challenges, even for state-of-the-art LLMs and LMs after fine-tuning. Further analyses reveal potential causes for the underperformance of LLMs and demonstrate that pre-training them on large-scale conceptualization taxonomies can potentially enhance their metaphysical reasoning capabilities. Our data and models are publicly accessible at https://github.com/HKUST-KnowComp/MARS.

Chain-of-thought reasoning, while powerful, can produce unnecessarily verbose output for simpler problems. We present a framework for difficulty-aware reasoning that teaches models to dynamically adjust reasoning depth based on problem complexity. Remarkably, we show that models can be endowed with such dynamic inference pathways without any architectural modifications; we simply post-train on data that is carefully curated to include chain-of-thought traces that are proportional in length to problem difficulty. Our analysis reveals that post-training via supervised fine-tuning (SFT) primarily captures patterns like reasoning length and format, while direct preference optimization (DPO) preserves reasoning accuracy, with their combination reducing length and maintaining or improving performance. Both quantitative metrics and qualitative assessments confirm that models can learn to "think proportionally", reasoning minimally on simple problems while maintaining depth for complex ones.

Recently, slow-thinking reasoning systems, such as o1, have demonstrated remarkable capabilities in solving complex reasoning tasks. These systems typically engage in an extended thinking process before responding to a query, allowing them to generate more thorough, accurate, and well-reasoned solutions. These systems are primarily developed and maintained by industry, with their core techniques not publicly disclosed. In response, an increasing number of studies from the research community aim to explore the technical foundations underlying these powerful reasoning systems. Building on these prior efforts, this paper presents a reproduction report on implementing o1-like reasoning systems. We introduce an "imitate, explore, and self-improve" framework as our primary technical approach to train the reasoning model. In the initial phase, we use distilled long-form thought data to fine-tune the reasoning model, enabling it to invoke a slow-thinking mode. The model is then encouraged to explore challenging problems by generating multiple rollouts, which can result in increasingly more high-quality trajectories that lead to correct answers. Furthermore, the model undergoes self-improvement by iteratively refining its training dataset. To verify the effectiveness of this approach, we conduct extensive experiments on three challenging benchmarks. The experimental results demonstrate that our approach achieves competitive performance compared to industry-level reasoning systems on these benchmarks.

Large reasoning models (LRMs) have achieved remarkable progress on complex tasks by generating extended chains of thought (CoT). However, their uncontrolled output lengths pose significant challenges for real-world deployment, where inference-time budgets on tokens, latency, or compute are strictly constrained. We propose Elastic Reasoning, a novel framework for scalable chain of thoughts that explicitly separates reasoning into two phases--thinking and solution--with independently allocated budgets. At test time, Elastic Reasoning prioritize that completeness of solution segments, significantly improving reliability under tight resource constraints. To train models that are robust to truncated thinking, we introduce a lightweight budget-constrained rollout strategy, integrated into GRPO, which teaches the model to reason adaptively when the thinking process is cut short and generalizes effectively to unseen budget constraints without additional training. Empirical results on mathematical (AIME, MATH500) and programming (LiveCodeBench, Codeforces) benchmarks demonstrate that Elastic Reasoning performs robustly under strict budget constraints, while incurring significantly lower training cost than baseline methods. Remarkably, our approach also produces more concise and efficient reasoning even in unconstrained settings. Elastic Reasoning offers a principled and practical solution to the pressing challenge of controllable reasoning at scale.

Hybrid reasoning systems that combine learned components with model-based inference are increasingly deployed in tool-augmented decision loops, yet their runtime behavior under partial observability and sustained evidence mismatch remains poorly understood. In practice, failures often arise as gradual divergence of internal reasoning dynamics rather than as isolated prediction errors. This work studies runtime stability in hybrid reasoning systems from a Kalman-inspired perspective. We model reasoning as a stochastic inference process driven by an internal innovation signal and introduce cognitive drift as a measurable runtime phenomenon. Stability is defined in terms of detectability, bounded divergence, and recoverability rather than task-level correctness. We propose a runtime stability framework that monitors innovation statistics, detects emerging instability, and triggers recovery-aware control mechanisms. Experiments on multi-step, tool-augmented reasoning tasks demonstrate reliable instability detection prior to task failure and show that recovery, when feasible, re-establishes bounded internal behavior within finite time. These results emphasize runtime stability as a system-level requirement for reliable reasoning under uncertainty.

Large reasoning models enhanced by reinforcement learning with verifiable rewards have achieved significant performance gains by extending their chain-of-thought. However, this paradigm incurs substantial deployment costs as models often exhibit excessive verbosity on simple queries. Existing efficient reasoning methods relying on explicit length penalties often introduce optimization conflicts and leave the generative mechanisms driving overthinking largely unexamined. In this paper, we identify a phenomenon termed length shift where models increasingly generate unnecessary reasoning on trivial inputs during training. To address this, we introduce Dynamic Outlier Truncation (DOT), a training-time intervention that selectively suppresses redundant tokens. This method targets only the extreme tail of response lengths within fully correct rollout groups while preserving long-horizon reasoning capabilities for complex problems. To complement this intervention and ensure stable convergence, we further incorporate auxiliary KL regularization and predictive dynamic sampling. Experimental results across multiple model scales demonstrate that our approach significantly pushes the efficiency-performance Pareto frontier outward. Notably, on the AIME-24, our method reduces inference token usage by 78% while simultaneously increasing accuracy compared to the initial policy and surpassing state-of-the-art efficient reasoning methods.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Large Language Models (LLMs) increasingly rely on prolonged reasoning chains to solve complex tasks. However, this trial-and-error approach often leads to high computational overhead and error propagation, where early mistakes can derail subsequent steps. To address these issues, we introduce Meta-Reasoner, a framework that dynamically optimizes inference-time reasoning by enabling LLMs to "think about how to think." Drawing inspiration from human meta-cognition and dual-process theory, Meta-Reasoner operates as a strategic advisor, decoupling high-level guidance from step-by-step generation. It employs "contextual multi-armed bandits" to iteratively evaluate reasoning progress, and select optimal strategies (e.g., backtrack, clarify ambiguity, restart from scratch, or propose alternative approaches), and reallocates computational resources toward the most promising paths. Our evaluations on mathematical reasoning and puzzles highlight the potential of dynamic reasoning chains to overcome inherent challenges in the LLM reasoning process and also show promise in broader applications, offering a scalable and adaptable solution for reasoning-intensive tasks.

Large Reasoning Models (LRMs) have demonstrated strong capabilities in complex multi-step reasoning, opening new opportunities for automating optimization modeling. However, existing domain adaptation methods, originally designed for earlier instruction-tuned models, often fail to exploit the advanced reasoning patterns of modern LRMs -- In particular, we show that direct fine-tuning on traditional non-reflective datasets leads to limited gains. To fully leverage LRMs' inherent reasoning abilities, we propose CALM (Corrective Adaptation with Lightweight Modification), a framework that progressively refines LRMs within their native reasoning modes for optimization modeling tasks. In CALM, an expert intervener identifies reasoning flaws and provides concise corrective hints, which the LRM incorporates to produce improved reasoning trajectories. These interventions modify fewer than 2.6\% of generated tokens, but generate high-quality data for soft adaptation through supervised fine-tuning. The adapted model is then further improved through reinforcement learning. Building on CALM, we develop STORM (Smart Thinking Optimization Reasoning Model), a 4B-parameter LRM that achieves a new state-of-the-art average accuracy of 68.9\% across five popular optimization modeling benchmarks, matching the performance of a 671B LRM. These results demonstrate that dynamic, hint-based data synthesis both preserves and amplifies the native reasoning patterns of modern LRMs, offering a more effective and scalable path towards expert-level performance on challenging optimization modeling tasks.

While LLMs have seen substantial improvement in reasoning capabilities, they also sometimes overthink, generating unnecessary reasoning steps, particularly under uncertainty, given ill-posed or ambiguous queries. We introduce statistically principled early stopping methods that monitor uncertainty signals during generation to mitigate this issue. Our first approach is parametric: it models inter-arrival times of uncertainty keywords as a renewal process and applies sequential testing for stopping. Our second approach is nonparametric and provides finite-sample guarantees on the probability of halting too early on well-posed queries. We conduct empirical evaluations on reasoning tasks across several domains and models. Our results indicate that uncertainty-aware early stopping can improve both efficiency and reliability in LLM reasoning, and we observe especially significant gains for math reasoning.

Recently, long-thought reasoning models achieve strong performance on complex reasoning tasks, but often incur substantial inference overhead, making efficiency a critical concern. Our empirical analysis reveals that the benefit of using Long-CoT varies across problems: while some problems require elaborate reasoning, others show no improvement, or even degraded accuracy. This motivates adaptive reasoning strategies that tailor reasoning depth to the input. However, prior work primarily reduces redundancy within long reasoning paths, limiting exploration of more efficient strategies beyond the Long-CoT paradigm. To address this, we propose a novel two-stage framework for adaptive and efficient reasoning. First, we construct a hybrid reasoning model by merging long and short CoT models to enable diverse reasoning styles. Second, we apply bi-level preference training to guide the model to select suitable reasoning styles (group-level), and prefer concise and correct reasoning within each style group (instance-level). Experiments demonstrate that our method significantly reduces inference costs compared to other baseline approaches, while maintaining performance. Notably, on five mathematical datasets, the average length of reasoning is reduced by more than 50%, highlighting the potential of adaptive strategies to optimize reasoning efficiency in large language models. Our code is coming soon at https://github.com/StarDewXXX/AdaR1

Reasoning LLMs often spend substantial tokens on long intermediate reasoning traces (e.g., chain-of-thought) when solving new problems. We propose to summarize and store reusable reasoning skills distilled from extensive deliberation and trial-and-error exploration, and to retrieve these skills at inference time to guide future reasoning. Unlike the prevailing reasoning from scratch paradigm, our approach first recalls relevant skills for each query, helping the model avoid redundant detours and focus on effective solution paths. We evaluate our method on coding and mathematical reasoning tasks, and find that it significantly reduces reasoning tokens while improving overall performance. The resulting lower per-request cost indicates strong practical and economic potential for real-world deployment.

Reasoning models have recently shown remarkable progress in domains such as math and coding. However, their expert-level abilities in math and coding contrast sharply with their performance in long-horizon, interactive tasks such as web navigation and computer/phone-use. Inspired by literature on human cognition, we argue that current AI agents need ''vicarious trial and error'' - the capacity to mentally simulate alternative futures before acting - in order to enhance their understanding and performance in complex interactive environments. We introduce Dyna-Mind, a two-stage training framework that explicitly teaches (V)LM agents to integrate such simulation into their reasoning. In stage 1, we introduce Reasoning with Simulations (ReSim), which trains the agent to generate structured reasoning traces from expanded search trees built from real experience gathered through environment interactions. ReSim thus grounds the agent's reasoning in faithful world dynamics and equips it with the ability to anticipate future states in its reasoning. In stage 2, we propose Dyna-GRPO, an online reinforcement learning method to further strengthen the agent's simulation and decision-making ability by using both outcome rewards and intermediate states as feedback from real rollouts. Experiments on two synthetic benchmarks (Sokoban and ALFWorld) and one realistic benchmark (AndroidWorld) demonstrate that (1) ReSim effectively infuses simulation ability into AI agents, and (2) Dyna-GRPO leverages outcome and interaction-level signals to learn better policies for long-horizon, planning-intensive tasks. Together, these results highlight the central role of simulation in enabling AI agents to reason, plan, and act more effectively in the ever more challenging environments.

Reasoning models enhance performance by tackling problems in a step-by-step manner, decomposing them into sub-problems and exploring long chains of thought before producing an answer. However, applying extended reasoning to every step introduces substantial redundancy, as sub-problems vary widely in difficulty and complexity: a small number of pivotal steps are genuinely challenging and decisive for the final answer, while many others only involve straightforward revisions or simple computations. Therefore, a natural idea is to endow reasoning models with the ability to adaptively respond to this variation, rather than treating all steps with the same level of elaboration. To this end, we propose MixReasoning, a framework that dynamically adjusts the depth of reasoning within a single response. The resulting chain of thought then becomes a mixture of detailed reasoning on difficult steps and concise inference on simpler ones. Experiments on GSM8K, MATH-500, and AIME show that MixReasoning shortens reasoning length and substantially improves efficiency without compromising accuracy.

Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. While human cognition fluidly adapts between intuitive, heuristic (System 1) and analytical, deliberative (System 2) reasoning depending on the context, LLMs lack this dynamic flexibility. This rigidity can lead to brittle and unreliable performance when faced with tasks that deviate from their trained patterns. To address this, we create a dataset of 2,000 samples with valid System 1 and System 2 answers, explicitly align LLMs with these reasoning styles, and evaluate their performance across reasoning benchmarks. Our results reveal an accuracy-efficiency trade-off: System 2-aligned models excel in arithmetic and symbolic reasoning, while System 1-aligned models perform better in commonsense tasks. A mechanistic analysis of model responses shows that System 1 models employ more definitive answers, whereas System 2 models demonstrate greater uncertainty. Interpolating between these extremes produces a monotonic transition in reasoning accuracy, preserving coherence. This work challenges the assumption that step-by-step reasoning is always optimal and highlights the need for adapting reasoning strategies based on task demands.

Recent advancements in large reasoning models (LRMs) have greatly improved their capabilities on complex reasoning tasks through Long Chains of Thought (CoTs). However, this approach often results in substantial redundancy, impairing computational efficiency and causing significant delays in real-time applications. Recent studies show that longer reasoning chains are frequently uncorrelated with correctness and can even be detrimental to accuracy. In a further in-depth analysis of this phenomenon, we surprisingly uncover and empirically verify that LRMs implicitly know the appropriate time to stop thinking, while this capability is obscured by current sampling paradigms. Motivated by this, we introduce SAGE (Self-Aware Guided Efficient Reasoning), a novel sampling paradigm that unleashes this efficient reasoning potential. Furthermore, integrating SAGE as mixed sampling into group-based reinforcement learning (SAGE-RL) enables SAGE-RL to effectively incorporate SAGE-discovered efficient reasoning patterns into standard pass@1 inference, markedly enhancing both the reasoning accuracy and efficiency of LRMs across multiple challenging mathematical benchmarks.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Recent advances in multimodal time series learning underscore a paradigm shift from analytics centered on basic patterns toward advanced time series understanding and reasoning. However, existing multimodal time series datasets mostly remain at the level of surface alignment and question answering, without reaching the depth of genuine reasoning. The absence of well-defined tasks that genuinely require time series reasoning, along with the scarcity of high-quality data, has limited progress in building practical time series reasoning models (TSRMs). To this end, we introduce Time Series Reasoning Suite (TSR-Suite), which formalizes four atomic tasks that span three fundamental capabilities for reasoning with time series: (1) perception, acquired through scenario understanding and causality discovery; (2) extrapolation, realized via event-aware forecasting; and (3) decision-making, developed through deliberation over perception and extrapolation. TSR-Suite is the first comprehensive time series reasoning suite that supports not only thorough evaluation but also the data pipeline and training of TSRMs. It contains more than 23K samples, of which 2.3K are carefully curated through a human-guided hierarchical annotation process. Building on this foundation, we introduce TimeOmni-1, the first unified reasoning model designed to address diverse real-world problems demanding time series reasoning. The model is trained in multiple stages, integrating a mixture of task scenarios, novel reward functions, and tailored optimizations. Experiments show that TimeOmni-1 delivers strong out-of-distribution generalization across all tasks and achieves a high rate of valid responses. It significantly improves causality discovery accuracy (64.0% vs. 35.9% with GPT-4.1) and raises the valid response rate by over 6% compared to GPT-4.1 on the event-aware forecasting task.

Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.

The output quality of large language models (LLMs) can be improved via "reasoning": generating segments of chain-of-thought (CoT) content to further condition the model prior to producing user-facing output. While these chains contain valuable information, they are verbose and lack explicit organization, making them tedious to review. Moreover, they lack opportunities for user feedback, such as to remove unwanted considerations, add desired ones, or clarify unclear assumptions. We introduce Interactive Reasoning, an interaction design that visualizes chain-of-thought outputs as a hierarchy of topics and enables user review and modification. We implement interactive reasoning in Hippo, a prototype for AI-assisted decision making in the face of uncertain trade-offs. In a user study with 16 participants, we find that interactive reasoning in Hippo allows users to quickly identify and interrupt erroneous generations, efficiently steer the model towards customized responses, and better understand both model reasoning and model outputs. Our work contributes to a new paradigm that incorporates user oversight into LLM reasoning processes.

Complex numerical time series analysis often demands multi-step reasoning capabilities beyond current models' reach. Tasks like medical diagnosis and weather forecasting require sequential reasoning processes - including counterfactual analysis, logical deduction, knowledge application, and multi-modal contextual integration - that existing time series models cannot explicitly perform. While recent research has shown large language models (LLMs) can achieve sophisticated Chain-of-Thought (CoT) reasoning through reinforcement learning (RL), these advances have primarily focused on mathematical and coding domains, with LLMs still demonstrating poor performance on time series tasks. We introduce Chain Of thought for Understanding Numerical Time Series (COUNTS), the first framework that trains LLMs to perform CoT reasoning across diverse time series tasks using RL with verifiable rewards. Our approach employs a Residual Vector-Quantized VAE to create high-fidelity discrete tokens that seamlessly integrate into a pre-trained LLM's vocabulary. COUNTS undergoes a two-stage training process: first, supervised fine-tuning on time series analysis tasks to master our novel representations, followed by Group Relative Policy Optimization training on verifiable problems using prompting strategies that encourage explicit reasoning steps before producing final answers. Our experiments demonstrate that this RL-driven approach with intermediate CoT reasoning significantly enhances LLM performance across various time series analysis tasks, opening new possibilities for complex temporal data reasoning.

The recent rise of Large Reasoning Models (LRMs) has significantly improved multi-step reasoning performance, but often at the cost of generating excessively long reasoning chains. This paper revisits the efficiency of such reasoning processes through an information-theoretic lens, revealing a fundamental trade-off between reasoning length and semantic efficiency. We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution, respectively. Empirical analyses show that longer reasoning chains tend to exhibit higher information bias and diminishing information gain, especially for incorrect answers. Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high, improving efficiency while maintaining competitive accuracy. Compared to the Vanilla Think approach (default mode), our strategy yields a 1.10% improvement in average accuracy and a 50.80% reduction in token usage on QwQ-32B across six benchmark tasks spanning diverse reasoning types and difficulty levels, demonstrating superior efficiency and reasoning performance. These results underscore the promise of entropy-based methods for enhancing both accuracy and cost-effiiciency in large language model deployment.

While Large Reasoning Models (LRMs) generate extensive chain-of-thought reasoning, we lack a principled framework for understanding how these thoughts are structured. In this paper, we introduce a novel approach by applying Schoenfeld's Episode Theory, a classic cognitive framework for human mathematical problem-solving, to analyze the reasoning traces of LRMs. We annotated thousands of sentences and paragraphs from model-generated solutions to math problems using seven cognitive labels (e.g., Plan, Implement, Verify). The result is the first publicly available benchmark for the fine-grained analysis of machine reasoning, including a large annotated corpus and detailed annotation guidebooks. Our preliminary analysis reveals distinct patterns in LRM reasoning, such as the transition dynamics between cognitive states. This framework provides a theoretically grounded methodology for interpreting LRM cognition and enables future work on more controllable and transparent reasoning systems.

Reasoning is a fundamental cognitive process underlying inference, problem-solving, and decision-making. While large language models (LLMs) demonstrate strong reasoning capabilities in closed-world settings, they struggle in open-ended and dynamic environments. Agentic reasoning marks a paradigm shift by reframing LLMs as autonomous agents that plan, act, and learn through continual interaction. In this survey, we organize agentic reasoning along three complementary dimensions. First, we characterize environmental dynamics through three layers: foundational agentic reasoning, which establishes core single-agent capabilities including planning, tool use, and search in stable environments; self-evolving agentic reasoning, which studies how agents refine these capabilities through feedback, memory, and adaptation; and collective multi-agent reasoning, which extends intelligence to collaborative settings involving coordination, knowledge sharing, and shared goals. Across these layers, we distinguish in-context reasoning, which scales test-time interaction through structured orchestration, from post-training reasoning, which optimizes behaviors via reinforcement learning and supervised fine-tuning. We further review representative agentic reasoning frameworks across real-world applications and benchmarks, including science, robotics, healthcare, autonomous research, and mathematics. This survey synthesizes agentic reasoning methods into a unified roadmap bridging thought and action, and outlines open challenges and future directions, including personalization, long-horizon interaction, world modeling, scalable multi-agent training, and governance for real-world deployment.

Despite the superior performance of Large Reasoning Models (LRMs), their reasoning behaviors are often counterintuitive, leading to suboptimal reasoning capabilities. To theoretically formalize the desired reasoning behaviors, this paper presents the Laws of Reasoning (LoRe), a unified framework that characterizes intrinsic reasoning patterns in LRMs. We first propose compute law with the hypothesis that the reasoning compute should scale linearly with question complexity. Beyond compute, we extend LoRe with a supplementary accuracy law. Since the question complexity is difficult to quantify in practice, we examine these hypotheses by two properties of the laws, monotonicity and compositionality. We therefore introduce LoRe-Bench, a benchmark that systematically measures these two tractable properties for large reasoning models. Evaluation shows that most reasoning models exhibit reasonable monotonicity but lack compositionality. In response, we develop an effective finetuning approach that enforces compute-law compositionality. Extensive empirical studies demonstrate that better compliance with compute laws yields consistently improved reasoning performance on multiple benchmarks, and uncovers synergistic effects across properties and laws. Project page: https://lore-project.github.io/

Large reasoning models (LRMs) show strong capabilities in complex reasoning, yet their marginal gains on evidence-dependent factual questions are limited. We find this limitation is partially attributable to a reasoning-answer hit gap, where the model identifies the correct facts during reasoning but fails to incorporate them into the final response, thereby reducing factual fidelity. To address this issue, we propose MR-ALIGN, a Meta-Reasoning informed alignment framework that enhances factuality without relying on external verifiers. MR-ALIGN quantifies state transition probabilities along the model's thinking process and constructs a transition-aware implicit reward that reinforces beneficial reasoning patterns while suppressing defective ones at the atomic thinking segments. This re-weighting reshapes token-level signals into probability-aware segment scores, encouraging coherent reasoning trajectories that are more conducive to factual correctness. Empirical evaluations across four factual QA datasets and one long-form factuality benchmark show that MR-ALIGN consistently improves accuracy and truthfulness while reducing misleading reasoning. These results highlight that aligning the reasoning process itself, rather than merely the outputs, is pivotal for advancing factuality in LRMs.

Recent advances in reasoning-centric language models have highlighted reinforcement learning (RL) as a promising method for aligning models with verifiable rewards. However, it remains contentious whether RL truly expands a model's reasoning capabilities or merely amplifies high-reward outputs already latent in the base model's distribution, and whether continually scaling up RL compute reliably leads to improved reasoning performance. In this work, we challenge prevailing assumptions by demonstrating that prolonged RL (ProRL) training can uncover novel reasoning strategies that are inaccessible to base models, even under extensive sampling. We introduce ProRL, a novel training methodology that incorporates KL divergence control, reference policy resetting, and a diverse suite of tasks. Our empirical analysis reveals that RL-trained models consistently outperform base models across a wide range of pass@k evaluations, including scenarios where base models fail entirely regardless of the number of attempts. We further show that reasoning boundary improvements correlates strongly with task competence of base model and training duration, suggesting that RL can explore and populate new regions of solution space over time. These findings offer new insights into the conditions under which RL meaningfully expands reasoning boundaries in language models and establish a foundation for future work on long-horizon RL for reasoning. We release model weights to support further research: https://huggingface.co/nvidia/Nemotron-Research-Reasoning-Qwen-1.5B

The emergence of Agentic AI systems has outpaced the architectural thinking required to operate them effectively. These agents differ fundamentally from traditional software: their behavior is not fixed at deployment but continuously shaped by experience, feedback, and context. Applying operational principles inherited from DevOps or MLOps, built for deterministic software and traditional ML systems, assumes that system behavior can be managed through versioning, monitoring, and rollback. This assumption breaks down for Agentic AI systems whose learning trajectories diverge over time. This introduces non-determinism making system reliability a challenge at runtime. We argue that architecting such systems requires a shift from managing control loops to enabling dynamic co-evolution among agents, infrastructure, and human oversight. To guide this shift, we introduce CHANGE, a conceptual framework comprising six capabilities for operationalizing Agentic AI systems: Contextualize, Harmonize, Anticipate, Negotiate, Generate, and Evolve. CHANGE provides a foundation for architecting an AgentOps platform to manage the lifecycle of evolving Agentic AI systems, illustrated through a customer-support system scenario. In doing so, CHANGE redefines software architecture for an era where adaptation to uncertainty and continuous evolution are inherent properties of the system.

As models increasingly leverage multi-step reasoning strategies to solve complex problems, supervising the logical validity of these intermediate steps has become a critical research challenge. Process reward models address this by providing step-by-step feedback, but current approaches have two major drawbacks: they typically function as classifiers without providing explanations, and their reliance on supervised fine-tuning with static datasets limits generalization. Inspired by recent advances, we reframe stepwise reward modeling from a classification task to a reasoning task itself. We thus propose a generative judge that reasons about the policy model's reasoning steps (i.e., meta-reasons), outputting thinking tokens before delivering a final verdict. Our model, StepWiser, is trained by reinforcement learning using relative outcomes of rollouts. We show it provides (i) better judgment accuracy on intermediate steps than existing methods; (ii) can be used to improve the policy model at training time; and (iii) improves inference-time search.

Rule-based reasoning has been acknowledged as one of the fundamental problems in reasoning, while deviations in rule formats, types, and complexity in real-world applications pose severe challenges. Recent studies have shown that large reasoning models (LRMs) have remarkable reasoning capabilities, and their performance is substantially enhanced by reinforcement learning (RL). However, it remains an open question whether small reasoning models (SRMs) can learn rule-based reasoning effectively with robust generalization across diverse tasks and domains. To address this, we introduce Reinforced Rule-based Reasoning, a.k.a. RuleReasoner, a simple yet effective method to conduct rule-based reasoning via a wide collection of curated tasks and a novel domain-aware dynamic sampling approach. Specifically, RuleReasoner resamples each training batch by updating the sampling weights of different domains based on historical rewards. This facilitates domain augmentation and flexible online learning schedules for RL, obviating the need for pre-hoc human-engineered mix-training recipes used in existing methods. Empirical evaluations on in-distribution (ID) and out-of-distribution (OOD) benchmarks reveal that RuleReasoner outperforms frontier LRMs by a significant margin (Delta4.1% average points on eight ID tasks and Delta10.4% average points on three OOD tasks over OpenAI-o1). Notably, our approach also exhibits higher computational efficiency compared to prior dynamic sampling methods for RL.

Hierarchical reasoning model (HRM) achieves extraordinary performance on various reasoning tasks, significantly outperforming large language model-based reasoners. To understand the strengths and potential failure modes of HRM, we conduct a mechanistic study on its reasoning patterns and find three surprising facts: (a) Failure of extremely simple puzzles, e.g., HRM can fail on a puzzle with only one unknown cell. We attribute this failure to the violation of the fixed point property, a fundamental assumption of HRM. (b) "Grokking" dynamics in reasoning steps, i.e., the answer is not improved uniformly, but instead there is a critical reasoning step that suddenly makes the answer correct; (c) Existence of multiple fixed points. HRM "guesses" the first fixed point, which could be incorrect, and gets trapped there for a while or forever. All facts imply that HRM appears to be "guessing" instead of "reasoning". Leveraging this "guessing" picture, we propose three strategies to scale HRM's guesses: data augmentation (scaling the quality of guesses), input perturbation (scaling the number of guesses by leveraging inference randomness), and model bootstrapping (scaling the number of guesses by leveraging training randomness). On the practical side, by combining all methods, we develop Augmented HRM, boosting accuracy on Sudoku-Extreme from 54.5% to 96.9%. On the scientific side, our analysis provides new insights into how reasoning models "reason".

Reasoning-oriented Large Language Models (LLMs) have achieved remarkable progress with Chain-of-Thought (CoT) prompting, yet they remain fundamentally limited by a blind self-thinking paradigm: performing extensive internal reasoning even when critical information is missing or ambiguous. We propose Proactive Interactive Reasoning (PIR), a new reasoning paradigm that transforms LLMs from passive solvers into proactive inquirers that interleave reasoning with clarification. Unlike existing search- or tool-based frameworks that primarily address knowledge uncertainty by querying external environments, PIR targets premise- and intent-level uncertainty through direct interaction with the user. PIR is implemented via two core components: (1) an uncertainty-aware supervised fine-tuning procedure that equips models with interactive reasoning capability, and (2) a user-simulator-based policy optimization framework driven by a composite reward that aligns model behavior with user intent. Extensive experiments on mathematical reasoning, code generation, and document editing demonstrate that PIR consistently outperforms strong baselines, achieving up to 32.70\% higher accuracy, 22.90\% higher pass rate, and 41.36 BLEU improvement, while reducing nearly half of the reasoning computation and unnecessary interaction turns. Further reliability evaluations on factual knowledge, question answering, and missing-premise scenarios confirm the strong generalization and robustness of PIR. Model and code are publicly available at: https://github.com/SUAT-AIRI/Proactive-Interactive-R1

Fine-tuning large language models (LLMs) on chain-of-thought (CoT) data shows that a small amount of high-quality data can outperform massive datasets. Yet, what constitutes "quality" remains ill-defined. Existing reasoning methods rely on indirect heuristics such as problem difficulty or trace length, while instruction-tuning has explored a broader range of automated selection strategies, but rarely in the context of reasoning. We propose to define reasoning data quality using influence functions, which measure the causal effect of individual CoT examples on downstream accuracy, and introduce influence-based pruning, which consistently outperforms perplexity and embedding-based baselines on math reasoning within a model family.

Recent advancements in reasoning with large language models (RLLMs), such as OpenAI-O1 and DeepSeek-R1, have demonstrated their impressive capabilities in complex domains like mathematics and coding. A central factor in their success lies in the application of long chain-of-thought (Long CoT) characteristics, which enhance reasoning abilities and enable the solution of intricate problems. However, despite these developments, a comprehensive survey on Long CoT is still lacking, limiting our understanding of its distinctions from traditional short chain-of-thought (Short CoT) and complicating ongoing debates on issues like "overthinking" and "test-time scaling." This survey seeks to fill this gap by offering a unified perspective on Long CoT. (1) We first distinguish Long CoT from Short CoT and introduce a novel taxonomy to categorize current reasoning paradigms. (2) Next, we explore the key characteristics of Long CoT: deep reasoning, extensive exploration, and feasible reflection, which enable models to handle more complex tasks and produce more efficient, coherent outcomes compared to the shallower Short CoT. (3) We then investigate key phenomena such as the emergence of Long CoT with these characteristics, including overthinking, and test-time scaling, offering insights into how these processes manifest in practice. (4) Finally, we identify significant research gaps and highlight promising future directions, including the integration of multi-modal reasoning, efficiency improvements, and enhanced knowledge frameworks. By providing a structured overview, this survey aims to inspire future research and further the development of logical reasoning in artificial intelligence.

Reasoning requires adaptation to novel problem settings under limited data and distribution shift. This work introduces CausalARC: an experimental testbed for AI reasoning in low-data and out-of-distribution regimes, modeled after the Abstraction and Reasoning Corpus (ARC). Each CausalARC reasoning task is sampled from a fully specified causal world model, formally expressed as a structural causal model. Principled data augmentations provide observational, interventional, and counterfactual feedback about the world model in the form of few-shot, in-context learning demonstrations. As a proof-of-concept, we illustrate the use of CausalARC for four language model evaluation settings: (1) abstract reasoning with test-time training, (2) counterfactual reasoning with in-context learning, (3) program synthesis, and (4) causal discovery with logical reasoning.

Evaluating large language models (LLMs) on final-answer correctness is the dominant paradigm. This approach, however, provides a coarse signal for model improvement and overlooks the quality of the underlying reasoning process. We argue that a more granular evaluation of reasoning offers a more effective path to building robust models. We decompose reasoning quality into two dimensions: relevance and coherence. Relevance measures if a step is grounded in the problem; coherence measures if it follows logically from prior steps. To measure these aspects reliably, we introduce causal stepwise evaluation (CaSE). This method assesses each reasoning step using only its preceding context, which avoids hindsight bias. We validate CaSE against human judgments on our new expert-annotated benchmarks, MRa-GSM8K and MRa-MATH. More importantly, we show that curating training data with CaSE-evaluated relevance and coherence directly improves final task performance. Our work provides a scalable framework for analyzing, debugging, and improving LLM reasoning, demonstrating the practical value of moving beyond validity checks.

Most work interpreting reasoning models studies only a single chain-of-thought (CoT), yet these models define distributions over many possible CoTs. We argue that studying a single sample is inadequate for understanding causal influence and the underlying computation. Though fully specifying this distribution is intractable, it can be understood by sampling. We present case studies using resampling to investigate model decisions. First, when a model states a reason for its action, does that reason actually cause the action? In "agentic misalignment" scenarios, we resample specific sentences to measure their downstream effects. Self-preservation sentences have small causal impact, suggesting they do not meaningfully drive blackmail. Second, are artificial edits to CoT sufficient for steering reasoning? These are common in literature, yet take the model off-policy. Resampling and selecting a completion with the desired property is a principled on-policy alternative. We find off-policy interventions yield small and unstable effects compared to resampling in decision-making tasks. Third, how do we understand the effect of removing a reasoning step when the model may repeat it post-edit? We introduce a resilience metric that repeatedly resamples to prevent similar content from reappearing downstream. Critical planning statements resist removal but have large effects when eliminated. Fourth, since CoT is sometimes "unfaithful", can our methods teach us anything in these settings? Adapting causal mediation analysis, we find that hints that have a causal effect on the output without being explicitly mentioned exert a subtle and cumulative influence on the CoT that persists even if the hint is removed. Overall, studying distributions via resampling enables reliable causal analysis, clearer narratives of model reasoning, and principled CoT interventions.

Large language models have demonstrated remarkable proficiency in long and complex reasoning tasks. However, they frequently exhibit a problematic reliance on familiar reasoning patterns, a phenomenon we term reasoning rigidity. Despite explicit instructions from users, these models often override clearly stated conditions and default to habitual reasoning trajectories, leading to incorrect conclusions. This behavior presents significant challenges, particularly in domains such as mathematics and logic puzzle, where precise adherence to specified constraints is critical. To systematically investigate reasoning rigidity, a behavior largely unexplored in prior work, we introduce a expert-curated diagnostic set, . Our dataset includes specially modified variants of existing mathematical benchmarks, namely AIME and MATH500, as well as well-known puzzles deliberately redesigned to require deviation from familiar reasoning strategies. Using this dataset, we identify recurring contamination patterns that occur when models default to ingrained reasoning. Specifically, we categorize this contamination into three distinctive modes: (i) Interpretation Overload, (ii) Input Distrust, and (iii) Partial Instruction Attention, each causing models to ignore or distort provided instructions. We publicly release our diagnostic set to facilitate future research on mitigating reasoning rigidity in language models.

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

Agents in the real world must make not only logical but also timely judgments. This requires continuous awareness of the dynamic environment: hazards emerge, opportunities arise, and other agents act, while the agent's reasoning is still unfolding. Despite advances in language model reasoning, existing approaches fail to account for this dynamic nature. We introduce real-time reasoning as a new problem formulation for agents in evolving environments and build Real-Time Reasoning Gym to demonstrate it. We study two paradigms for deploying language models in agents: (1) reactive agents, which employ language models with bounded reasoning computation for rapid responses, and (2) planning agents, which allow extended reasoning computation for complex problems. Our experiments show that even state-of-the-art models struggle with making logical and timely judgments in either paradigm. To address this limitation, we propose AgileThinker, which simultaneously engages both reasoning paradigms. AgileThinker consistently outperforms agents engaging only one reasoning paradigm as the task difficulty and time pressure rise, effectively balancing reasoning depth and response latency. Our work establishes real-time reasoning as a critical testbed for developing practical agents and provides a foundation for research in temporally constrained AI systems, highlighting a path toward real-time capable agents.

Time series data is ubiquitous in real-world scenarios and crucial for critical applications ranging from energy management to traffic control. Consequently, the ability to reason over time series is a fundamental skill for generalist models to solve practical problems. However, this dimension is notably absent from existing benchmarks of generalist models. To bridge this gap, we introduce TSRBench, a comprehensive multi-modal benchmark designed to stress-test the full spectrum of time series reasoning capabilities. TSRBench features: i) a diverse set of 4125 problems from 14 domains, and is categorized into 4 major dimensions: Perception, Reasoning, Prediction, and Decision-Making. ii) 15 tasks from the 4 dimensions evaluating essential reasoning capabilities (e.g., numerical reasoning). Through extensive experiments, we evaluated over 30 leading proprietary and open-source LLMs, VLMs, and TSLLMs within TSRBench. Our findings reveal that: i) scaling laws hold for perception and reasoning but break down for prediction; ii) strong reasoning does not guarantee accurate context-aware forecasting, indicating a decoupling between semantic understanding and numerical prediction; and iii) despite the complementary nature of textual and visual represenations of time series as inputs, current multimodal models fail to effectively fuse them for reciprocal performance gains. TSRBench provides a standardized evaluation platform that not only highlights existing challenges but also offers valuable insights to advance generalist models. Our code and dataset are available at https://tsrbench.github.io/.

We introduce Vibe Reasoning, a human-AI collaborative paradigm for solving complex mathematical problems. Our key insight is that frontier AI models already possess the knowledge required to solve challenging problems -- they simply do not know how, what, or when to apply it. Vibe Reasoning transforms AI's latent potential into manifested capability through generic meta-prompts, agentic grounding, and model orchestration. We demonstrate this paradigm through IMO 2025 Problem 6, a combinatorial optimization problem where autonomous AI systems publicly reported failures. Our solution combined GPT-5's exploratory capabilities with Gemini 3 Pro's proof strengths, leveraging agentic workflows with Python code execution and file-based memory, to derive both the correct answer (2112) and a rigorous mathematical proof. Through iterative refinement across multiple attempts, we discovered the necessity of agentic grounding and model orchestration, while human prompts evolved from problem-specific hints to generic, transferable meta-prompts. We analyze why capable AI fails autonomously, how each component addresses specific failure modes, and extract principles for effective vibe reasoning. Our findings suggest that lightweight human guidance can unlock frontier models' mathematical reasoning potential. This is ongoing work; we are developing automated frameworks and conducting broader evaluations to further validate Vibe Reasoning's generality and effectiveness.

Despite achieving high accuracy on medical benchmarks, LLMs exhibit the Einstellung Effect in clinical diagnosis--relying on statistical shortcuts rather than patient-specific evidence, causing misdiagnosis in atypical cases. Existing benchmarks fail to detect this critical failure mode. We introduce MedEinst, a counterfactual benchmark with 5,383 paired clinical cases across 49 diseases. Each pair contains a control case and a "trap" case with altered discriminative evidence that flips the diagnosis. We measure susceptibility via Bias Trap Rate--probability of misdiagnosing traps despite correctly diagnosing controls. Extensive Evaluation of 17 LLMs shows frontier models achieve high baseline accuracy but severe bias trap rates. Thus, we propose ECR-Agent, aligning LLM reasoning with Evidence-Based Medicine standard via two components: (1) Dynamic Causal Inference (DCI) performs structured reasoning through dual-pathway perception, dynamic causal graph reasoning across three levels (association, intervention, counterfactual), and evidence audit for final diagnosis; (2) Critic-Driven Graph and Memory Evolution (CGME) iteratively refines the system by storing validated reasoning paths in an exemplar base and consolidating disease-specific knowledge into evolving illness graphs. Source code is to be released.

Deep iterative chain-of-thought (CoT) reasoning enables LLMs to tackle complex tasks by progressively activating relevant pre-trained knowledge. However, it faces challenges in ensuring continual improvement and determining a stopping criterion. In this paper, we investigate whether the relevant knowledge that contributes directly to solving the given question can be activated from the initial reasoning path, thus circumventing the need for iterative refinement. Our experiments reveal that increasing the diversity of initial reasoning paths can achieve comparable or superior performance, a concept we term breadth reasoning. However, existing breadth reasoning approaches, such as self-consistency, offer limited diversity. To address this limitation, we propose a simple yet effective method that enhances reasoning breadth by integrating contextual exploration with reduced sampling randomness. Extensive experiments demonstrate that our approach significantly outperforms deep iterative reasoning. Our code is provided in https://github.com/zongqianwu/breadth.

We present Hermes 4, a family of hybrid reasoning models that combine structured, multi-turn reasoning with broad instruction-following ability. We describe the challenges encountered during data curation, synthesis, training, and evaluation, and outline the solutions employed to address these challenges at scale. We comprehensively evaluate across mathematical reasoning, coding, knowledge, comprehension, and alignment benchmarks, and we report both quantitative performance and qualitative behavioral analysis. To support open research, all model weights are published publicly at https://huggingface.co/collections/NousResearch/hermes-4-collection-68a731bfd452e20816725728

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to move beyond fast System-1 responses and engage in deliberative System-2 reasoning. However, this comes at the cost of significant inefficiency due to verbose intermediate output. Recent latent-space reasoning methods improve efficiency by operating on hidden states without decoding into language, yet they treat all steps uniformly, failing to distinguish critical deductions from auxiliary steps and resulting in suboptimal use of computational resources. In this paper, we propose System-1.5 Reasoning, an adaptive reasoning framework that dynamically allocates computation across reasoning steps through shortcut paths in latent space. Specifically, System-1.5 Reasoning introduces two types of dynamic shortcuts. The model depth shortcut (DS) adaptively reasons along the vertical depth by early exiting non-critical tokens through lightweight adapter branches, while allowing critical tokens to continue through deeper Transformer layers. The step shortcut (SS) reuses hidden states across the decoding steps to skip trivial steps and reason horizontally in latent space. Training System-1.5 Reasoning involves a two-stage self-distillation process: first distilling natural language CoT into latent-space continuous thought, and then distilling full-path System-2 latent reasoning into adaptive shortcut paths (System-1.5 Reasoning). Experiments on reasoning tasks demonstrate the superior performance of our method. For example, on GSM8K, System-1.5 Reasoning achieves reasoning performance comparable to traditional CoT fine-tuning methods while accelerating inference by over 20x and reducing token generation by 92.31% on average.

While Test-Time Scaling (TTS) has proven effective in improving the reasoning ability of large language models (LLMs), low diversity in model outputs often becomes a bottleneck; this is partly caused by the common "one problem, one solution" (1P1S) training practice, which provides a single canonical answer and can push models toward a narrow set of reasoning paths. This homogenization not only limits sampling effectiveness but also restricts the exploration space for subsequent Reinforcement Learning (RL) stages. To address this, we propose a "one problem, multiple solutions" (1PNS) training paradigm that exposes the model to a variety of valid reasoning trajectories and thus increases inference diversity. A core challenge for 1PNS is reliably measuring semantic differences between multi-step chains of thought, so we introduce Reasoning Path Divergence (RPD), a step-level metric that aligns and scores Long Chain-of-Thought solutions to capture differences in intermediate reasoning. Using RPD, we curate maximally diverse solution sets per problem and fine-tune Qwen3-4B-Base. Experiments show that RPD-selected training yields more varied outputs and higher pass@k, with an average +2.80% gain in pass@16 over a strong 1P1S baseline and a +4.99% gain on AIME24, demonstrating that 1PNS further amplifies the effectiveness of TTS. Our code is available at https://github.com/fengjujf/Reasoning-Path-Divergence .

Recent advancements in large language models (LLMs) often rely on generating intermediate reasoning steps to enhance accuracy. However, little work has examined how reasoning utility contributes to the final answer's correctness. Due to the stochastic nature of autoregressive generation, generating more context does not guarantee increased confidence in the answer. If we could predict, during generation, whether a reasoning step will be useful, we could stop early or prune ineffective steps, avoiding distractions in the final decision. We present an oracle study on MATH dataset, using Qwen2.5-32B and GPT-4o to generate reasoning chains, and then employing a separate model (Qwen3-8B) to quantify the utility of these chains for final accuracy. Specifically, we measure the model's uncertainty on the answer span Y at each reasoning step using conditional entropy (expected negative log-likelihood over the vocabulary) with context expanding step by step. Our results show a clear pattern: conditional entropy that decreases over steps is strongly associated with correct answers, whereas flat or increasing entropy often results in wrong answers. We also corroborate that incorrect reasoning paths tend to be longer than correct ones, suggesting that longer reasoning does not necessarily yield better outcomes. These findings serve as a foundation to inspire future work on designing efficient reasoning pipelines that detect and avoid unproductive reasoning early.

While Large Language Models (LLMs) achieve high performance on standard mathematical benchmarks, their underlying reasoning processes remain highly overfit to standard textual formatting. We propose a perturbation pipeline consisting of 14 techniques to evaluate robustness of LLM reasoning. We apply this pipeline to AIME 2024 dataset and evalute 8 state-of-the-art models on the resulting benchmark. While frontier models exhibit resilience, open weights reasoning models suffer catastrophic collapses (up to 55% average accuracy drops across perturbations and up to 100% on some), exposing structural fragility. To further disentangle mechanical parsing failures from downstream reasoning failures, we strictly isolate the models' working memory capacity by forcing models to solve multiple unperturbed mathematical problems sequentially within a single context window. Our results indicate that open weight models ranging from 7B to 120B parameters and Claude Opus 4.6 exhibit accuracy decay on subsequent problems. This degradation demonstrates that intermediate reasoning steps permanently pollute standard dense attention mechanisms. We argue that to achieve reliable reasoning, future reasoning architectures must integrate explicit contextual resets within a model's own Chain-of-Thought, leading to fundamental open questions regarding the optimal granularity of atomic reasoning tasks.

Understanding uncertainty in chain-of-thought reasoning is critical for reliable deployment of large language models. In this work, we propose a simple yet effective diagnostic approach based on trajectory shape rather than scalar magnitude. We show that this signal is practical, interpretable, and inexpensive to obtain in black-box settings, while remaining robust across models and datasets. Through extensive ablations and cross-domain replications, we demonstrate its utility for selective prediction and triage. Our findings offer a generalizable insight into uncertainty dynamics in reasoning tasks, with particular focus on numeric and discrete-answer settings.

Achieving human-level intelligence requires refining the transition from the fast, intuitive System 1 to the slower, more deliberate System 2 reasoning. While System 1 excels in quick, heuristic decisions, System 2 relies on logical reasoning for more accurate judgments and reduced biases. Foundational Large Language Models (LLMs) excel at fast decision-making but lack the depth for complex reasoning, as they have not yet fully embraced the step-by-step analysis characteristic of true System 2 thinking. Recently, reasoning LLMs like OpenAI's o1/o3 and DeepSeek's R1 have demonstrated expert-level performance in fields such as mathematics and coding, closely mimicking the deliberate reasoning of System 2 and showcasing human-like cognitive abilities. This survey begins with a brief overview of the progress in foundational LLMs and the early development of System 2 technologies, exploring how their combination has paved the way for reasoning LLMs. Next, we discuss how to construct reasoning LLMs, analyzing their features, the core methods enabling advanced reasoning, and the evolution of various reasoning LLMs. Additionally, we provide an overview of reasoning benchmarks, offering an in-depth comparison of the performance of representative reasoning LLMs. Finally, we explore promising directions for advancing reasoning LLMs and maintain a real-time https://github.com/zzli2022/Awesome-Slow-Reason-System{GitHub Repository} to track the latest developments. We hope this survey will serve as a valuable resource to inspire innovation and drive progress in this rapidly evolving field.

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic techniques and mathematical reasoning.

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR

Large reasoning models (LRMs) like OpenAI o1 and DeepSeek R1 have demonstrated impressive performance on complex reasoning tasks like mathematics and programming with long Chain-of-Thought (CoT) reasoning sequences (slow-thinking), compared with traditional large language models (fast-thinking). However, these reasoning models also face a huge challenge that generating unnecessarily lengthy and redundant reasoning chains even for trivial questions. This phenomenon leads to a significant waste of inference resources, increases the response time for simple queries, and hinders the practical application of LRMs in real-world products. To this end, it is crucial to shorten lengthy reasoning chains and learn adaptive reasoning between fast and slow thinking based on input difficulty. In this survey, we provide a comprehensive overview of recent progress in concise and adaptive thinking for efficient reasoning of LRMs, including methodologies, benchmarks, and challenges for future exploration. We hope this survey can help researchers quickly understand the landscape of this field and inspire novel adaptive thinking ideas to facilitate better usage of LRMs.

Do reasoning models have "Aha!" moments? Prior work suggests that models like DeepSeek-R1-Zero undergo sudden mid-trace realizations that lead to accurate outputs, implying an intrinsic capacity for self-correction. Yet, it remains unclear whether such intrinsic shifts in reasoning strategy actually improve performance. Here, we study mid-reasoning shifts and instrument training runs to detect them. Our analysis spans 1M+ reasoning traces, hundreds of training checkpoints, three reasoning domains, and multiple decoding temperatures and model architectures. We find that reasoning shifts are rare, do not become more frequent with training, and seldom improve accuracy, indicating that they do not correspond to prior perceptions of model insight. However, their effect varies with model uncertainty. Building on this finding, we show that artificially triggering extrinsic shifts under high entropy reliably improves accuracy. Our results show that mid-reasoning shifts are symptoms of unstable inference behavior rather than an intrinsic mechanism for self-correction.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

We introduce S1-Bench, a novel benchmark designed to evaluate Large Reasoning Models' (LRMs) performance on simple tasks that favor intuitive system 1 thinking rather than deliberative system 2 reasoning. While LRMs have achieved significant breakthroughs in complex reasoning tasks through explicit chains of thought, their reliance on deep analytical thinking may limit their system 1 thinking capabilities. Moreover, a lack of benchmark currently exists to evaluate LRMs' performance in tasks that require such capabilities. To fill this gap, S1-Bench presents a set of simple, diverse, and naturally clear questions across multiple domains and languages, specifically designed to assess LRMs' performance in such tasks. Our comprehensive evaluation of 22 LRMs reveals significant lower efficiency tendencies, with outputs averaging 15.5 times longer than those of traditional small LLMs. Additionally, LRMs often identify correct answers early but continue unnecessary deliberation, with some models even producing numerous errors. These findings highlight the rigid reasoning patterns of current LRMs and underscore the substantial development needed to achieve balanced dual-system thinking capabilities that can adapt appropriately to task complexity.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). However, a critical paradox clouds its efficacy: RLVR-tuned models often underperform their base models on the Pass@K metric for solution-finding, leading to the hypothesis that RLVR merely re-weights existing reasoning paths at the cost of reasoning diversity. In this work, we resolve this contradiction by identifying the source of the problem: the Pass@K metric itself is a flawed measure of reasoning, as it credits correct final answers that probably arise from inaccurate or incomplete chains of thought (CoTs). To address this, we introduce a more precise evaluation metric, CoT-Pass@K, which mandates that both the reasoning path and the final answer be correct. We provide a new theoretical foundation that formalizes how RLVR, unlike traditional RL, is uniquely structured to incentivize logical integrity. Our empirical results are supportive: using CoT-Pass@K, we observe that RLVR can incentivize the generalization of correct reasoning for all values of K. Furthermore, by analyzing the training dynamics, we find that this enhanced reasoning capability emerges early in the training process and smoothly generalizes. Our work provides a clear perspective on the role of RLVR, offers a more reliable method for its evaluation, and confirms its potential to genuinely advance machine reasoning.

While Large Language Models (LLMs) have demonstrated their proficiency in complex reasoning tasks, their performance in dynamic, interactive, and competitive scenarios - such as business strategy and stock market analysis - remains underexplored. To bridge this gap, we formally explore the dynamic reasoning capabilities of LLMs for decision-making in rapidly evolving environments. We introduce two game theory-based pilot challenges that mirror the complexities of real-world dynamic decision-making. These challenges are well-defined, enabling clear, controllable, and precise evaluation of LLMs' dynamic reasoning abilities. Through extensive experiments, we find that existing reasoning methods tend to falter in dynamic settings that require k-level thinking - a key concept not tackled by previous works. To address this, we propose a novel reasoning approach for LLMs, named "K-Level Reasoning". This approach adopts the perspective of rivals to recursively employ k-level thinking based on available historical information, which significantly improves the prediction accuracy of rivals' subsequent moves and informs more strategic decision-making. This research not only sets a robust quantitative benchmark for the assessment of dynamic reasoning but also markedly enhances the proficiency of LLMs in dynamic contexts.

Recent advances in reasoning-centric models promise improved robustness through mechanisms such as chain-of-thought prompting and test-time scaling. However, their ability to withstand misleading user input remains underexplored. In this paper, we conduct a systematic evaluation of three state-of-the-art reasoning models, i.e., OpenAI's o4-mini, Claude-3.7-Sonnet and Gemini-2.5-Flash, across three multimodal benchmarks: MMMU, MathVista, and CharXiv. Our evaluation reveals significant accuracy drops (25-29% on average) following gaslighting negation prompts, indicating that even top-tier reasoning models struggle to preserve correct answers under manipulative user feedback. Built upon the insights of the evaluation and to further probe this vulnerability, we introduce GaslightingBench-R, a new diagnostic benchmark specifically designed to evaluate reasoning models' susceptibility to defend their belief under gaslighting negation prompt. Constructed by filtering and curating 1,025 challenging samples from the existing benchmarks, GaslightingBench-R induces even more dramatic failures, with accuracy drops exceeding 53% on average. Our findings reveal fundamental limitations in the robustness of reasoning models, highlighting the gap between step-by-step reasoning and belief persistence.

O1/R1 style large reasoning models (LRMs) signal a substantial leap forward over conventional instruction-following LLMs. By applying test-time scaling to generate extended reasoning paths, they establish many SOTAs across a wide range of complex reasoning tasks. However, recent studies show that LRMs are prone to suffer from overthinking -- the tendency to overcomplicate simple problems, leading to excessive strategy switching and long, convoluted reasoning traces that hinder their interpretability. To mitigate this issue, we conduct a systematic investigation into the reasoning efficiency of a broad set of LRMs and uncover a common dilemma: the difficulty in balancing multiple generation objectives such as correctness and brevity. Based on this discovery, we propose a test-time scaling method, EDIT (Efficient Dynamic Inference Trimming), which efficiently guides LRMs to identify the shortest correct reasoning paths at test time. EDIT employs constraint-guided generation while jointly tracking length and answer distributions under varying constraints, allowing it to select responses that strike an optimal balance between conciseness and correctness. Extensive experiments across diverse models and datasets show that EDIT substantially enhance the reasoning efficiency, producing compact yet informative outputs that improve readability and user experience.

Large Reasoning Models (LRMs) exhibit strong performance, yet often produce rationales that sound plausible but fail to reflect their true decision process, undermining reliability and trust. We introduce a formal framework for reasoning faithfulness, defined by two testable conditions: stance consistency (a coherent stance linking reasoning to answer) and causal influence (the stated reasoning causally drives the answer under output-level interventions), explicitly decoupled from accuracy. To operationalize this, we present RFEval, a benchmark of 7,186 instances across seven tasks that probes faithfulness via controlled, output-level counterfactual interventions. Evaluating twelve open-source LRMs, we find unfaithfulness in 49.7% of outputs, predominantly from stance inconsistency. Failures are concentrated in brittle, convergent domains such as math and code, and correlate more with post-training regimes than with scale: within-family ablations indicate that adding current RL-style objectives on top of supervised fine-tuning can reduce reasoning faithfulness, even when accuracy is maintained. Crucially, accuracy is neither a sufficient nor a reliable proxy for faithfulness: once controlling for model and task, the accuracy-faithfulness link is weak and statistically insignificant. Our work establishes a rigorous methodology for auditing LRM reliability and shows that trustworthy AI requires optimizing not only for correct outcomes but also for the structural integrity of the reasoning process. Our code and dataset can be found at project page: https://aidaslab.github.io/RFEval/}{https://aidaslab.github.io/RFEval/

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

In recent years, reinforcement learning (RL) has emerged as a popular approach for solving sequence-based tasks in machine learning. However, finding suitable alternatives to RL remains an exciting and innovative research area. One such alternative that has garnered attention is the Non-Axiomatic Reasoning System (NARS), which is a general-purpose cognitive reasoning framework. In this paper, we delve into the potential of NARS as a substitute for RL in solving sequence-based tasks. To investigate this, we conduct a comparative analysis of the performance of ONA as an implementation of NARS and Q-Learning in various environments that were created using the Open AI gym. The environments have different difficulty levels, ranging from simple to complex. Our results demonstrate that NARS is a promising alternative to RL, with competitive performance in diverse environments, particularly in non-deterministic ones.

With the advent of DeepSeek-R1, a new wave of reinforcement learning (RL) methods has emerged that seem to unlock stronger mathematical reasoning. However, a closer look at the open-source ecosystem reveals a critical limitation: with sufficiently many draws (e.g., pass@1024), many existing base models already solve nearly all questions on widely used math benchmarks such as MATH-500 and AIME 2024. This suggests that the RL fine-tuning methods prevalent in the LLM reasoning literature largely sharpen existing solution modes rather than discovering entirely new ones. Such sharpening stands in contrast to the broader promise of RL: to foster exploration and to acquire new skills. To move beyond this plateau, we introduce MATH-Beyond (MATH-B), a benchmark deliberately constructed to defeat common open-source models of up to 8B parameters even under large sampling budgets. Improving performance on our benchmark via RL requires methods that learn to reason in ways that go beyond base model capabilities in repeated sampling. Since the problems are drawn from subsets of DAPO-Math-17K and DeepScaleR datasets, they remain topically equivalent to standard high-school math. Validating our premise, RL fine-tuned models such as Nemotron-Research-Reasoning-Qwen-1.5B and DeepScaleR-1.5B-Preview perform poorly on MATH-B at pass@1024, showing how existing approaches fall short on tackling harder instances. We hope MATH-B will catalyze exploration-driven RL approaches that elicit deeper reasoning capabilities. We release MATH-B at https://huggingface.co/datasets/brendel-group/MATH-Beyond.

Test-time scaling has emerged as a transformative paradigm for enhancing the performance of large reasoning models, enabling dynamic allocation of computational resources during inference. However, as the landscape of reasoning models rapidly expands, a critical question remains: how can we systematically compare and evaluate the test-time scaling capabilities across different models? In this paper, we introduce ARISE (Adaptive Resolution-aware Scaling Evaluation), a novel metric specifically designed to assess the test-time scaling effectiveness of large reasoning models. Unlike existing evaluation approaches, ARISE incorporates two key innovations: (1) sample-level awareness that effectively penalizes negative scaling behaviors where increased computation leads to performance degradation, and (2) a dynamic sampling mechanism that mitigates the impact of accuracy fluctuations and token count instability on the final assessment. We conduct comprehensive experiments evaluating state-of-the-art reasoning models across diverse domains including mathematical reasoning, code generation, and agentic tasks. Our results demonstrate that ARISE provides a reliable and fine-grained measurement of test-time scaling capabilities, revealing significant variations in scaling efficiency across models. Notably, our evaluation identifies Claude Opus as exhibiting superior scaling characteristics compared to other contemporary reasoning models.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Large language models (LLMs) have been routinely used to solve various tasks using step-by-step reasoning. However, the structure of intermediate reasoning steps, or thoughts, is rigid and unidirectional, such as chains, trees, or acyclic-directed graphs. Consequently, the resulting inflexible and forward-only reasoning may not address challenging tasks and fail when the LLM frequently gives false responses, i.e., ``hallucinations''. This paper proposes a new reasoning framework, called Thought Rollback (TR), allowing LLMs to adaptively build thought structure while maintaining effective reasoning toward problem-solving under ``hallucinations''. The core mechanism of TR is rolling back thoughts, which allows LLMs to perform error analysis on thoughts, and thus roll back to any previously mistaken thought for revision. Subsequently, by including such trial-and-error in the prompt to guide the LLM, each rollback leads to one more reliable reasoning path. Therefore, starting with a simple prompt without human annotations, LLM with TR adaptively and gradually explores thoughts for a correct solution. Comprehensive experiments on mathematical problems and multi-task reasoning demonstrate the state-of-the-art performance of TR in terms of problem-solving rate and interaction cost. For instance, the solving rate of GPT-4 with TR outperforms the current best by 9% on the MATH dataset.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in large reasoning models. To analyze reasoning dynamics, we use synthetic logic puzzles as training data due to their controllable complexity and straightforward answer verification. We make some key technical contributions that lead to effective and stable RL training: a system prompt that emphasizes the thinking and answering process, a stringent format reward function that penalizes outputs for taking shortcuts, and a straightforward training recipe that achieves stable convergence. Our 7B model develops advanced reasoning skills-such as reflection, verification, and summarization-that are absent from the logic corpus. Remarkably, after training on just 5K logic problems, it demonstrates generalization abilities to the challenging math benchmarks AIME and AMC.

Recent advanced large reasoning models (LRMs) leverage extended chain-of-thought (CoT) reasoning to solve complex tasks, achieving state-of-the-art performance. Despite their success, we identify a critical issue: a substantial portion of simple tasks solved by LRMs can also be addressed by non-reasoning LLMs using significantly fewer tokens, indicating the complex reasoning may not always be necessary. To address this, we systematically analyze the reasoning trajectories of LRMs and present a method utilizing identified paradigms and LLM-Judge to classify these trajectories as either Redundant Reasoning or Essential Reasoning. And we introduce OThink-R1, a method that prunes redundant reasoning steps while preserving logical validity. OThink-R1 dynamically employs the non-thinking mode (fast-thinking) for straightforward problems while engaging in deliberate thinking (slow-thinking) for complex problems. Experiments across mathematical and question-answering tasks demonstrate that OThink-R1 reduces reasoning redundancy by almost 23\% on average without compromising accuracy, offering practical guidelines for efficient reasoning models. The code is available at https://github.com/AgenticIR-Lab/OThink-R1.

Large Reasoning Models (LRMs) have significantly enhanced their capabilities in complex problem-solving by introducing a thinking draft that enables multi-path Chain-of-Thought explorations before producing final answers. Ensuring the faithfulness of these intermediate reasoning processes is crucial for reliable monitoring, interpretation, and effective control. In this paper, we propose a systematic counterfactual intervention framework to rigorously evaluate thinking draft faithfulness. Our approach focuses on two complementary dimensions: (1) Intra-Draft Faithfulness, which assesses whether individual reasoning steps causally influence subsequent steps and the final draft conclusion through counterfactual step insertions; and (2) Draft-to-Answer Faithfulness, which evaluates whether final answers are logically consistent with and dependent on the thinking draft, by perturbing the draft's concluding logic. We conduct extensive experiments across six state-of-the-art LRMs. Our findings show that current LRMs demonstrate selective faithfulness to intermediate reasoning steps and frequently fail to faithfully align with the draft conclusions. These results underscore the need for more faithful and interpretable reasoning in advanced LRMs.

We introduce Phi-4-reasoning, a 14-billion parameter reasoning model that achieves strong performance on complex reasoning tasks. Trained via supervised fine-tuning of Phi-4 on carefully curated set of "teachable" prompts-selected for the right level of complexity and diversity-and reasoning demonstrations generated using o3-mini, Phi-4-reasoning generates detailed reasoning chains that effectively leverage inference-time compute. We further develop Phi-4-reasoning-plus, a variant enhanced through a short phase of outcome-based reinforcement learning that offers higher performance by generating longer reasoning traces. Across a wide range of reasoning tasks, both models outperform significantly larger open-weight models such as DeepSeek-R1-Distill-Llama-70B model and approach the performance levels of full DeepSeek-R1 model. Our comprehensive evaluations span benchmarks in math and scientific reasoning, coding, algorithmic problem solving, planning, and spatial understanding. Interestingly, we observe a non-trivial transfer of improvements to general-purpose benchmarks as well. In this report, we provide insights into our training data, our training methodologies, and our evaluations. We show that the benefit of careful data curation for supervised fine-tuning (SFT) extends to reasoning language models, and can be further amplified by reinforcement learning (RL). Finally, our evaluation points to opportunities for improving how we assess the performance and robustness of reasoning models.

Reasoning models improve their problem-solving ability through inference-time scaling, allocating more compute via longer token budgets. Identifying which reasoning traces are likely to succeed remains a key opportunity: reliably predicting productive paths can substantially reduce wasted computation and improve overall efficiency. We introduce Latent-Trajectory signals that characterize the temporal evolution of a model's internal representations during the generation of intermediate reasoning tokens. By measuring the overall change in latent representations between the start and end of reasoning, the change accumulated across intermediate steps, and the extent to which these changes advance toward the final state, we show that these signals predict solution accuracy more reliably than both cross-layer metrics and output-based confidence measures. When used to guide answer selection across multiple sampled generations, Latent-Trajectory signals make test-time scaling more effective and efficient than majority voting, reducing token usage by up to 70% while preserving and even improving accuracy by 2.6% on average. Moreover, these predictive signals often emerge early in the reasoning trace, enabling early selection and allocation of compute to the most promising candidates. Our findings contribute not only practical strategies for inference-time efficiency, but also a deeper interpretability perspective on how reasoning processes are represented and differentiated in latent space.

Reasoning is a fundamental cognitive process that enables logical inference, problem-solving, and decision-making. With the rapid advancement of large language models (LLMs), reasoning has emerged as a key capability that distinguishes advanced AI systems from conventional models that empower chatbots. In this survey, we categorize existing methods along two orthogonal dimensions: (1) Regimes, which define the stage at which reasoning is achieved (either at inference time or through dedicated training); and (2) Architectures, which determine the components involved in the reasoning process, distinguishing between standalone LLMs and agentic compound systems that incorporate external tools, and multi-agent collaborations. Within each dimension, we analyze two key perspectives: (1) Input level, which focuses on techniques that construct high-quality prompts that the LLM condition on; and (2) Output level, which methods that refine multiple sampled candidates to enhance reasoning quality. This categorization provides a systematic understanding of the evolving landscape of LLM reasoning, highlighting emerging trends such as the shift from inference-scaling to learning-to-reason (e.g., DeepSeek-R1), and the transition to agentic workflows (e.g., OpenAI Deep Research, Manus Agent). Additionally, we cover a broad spectrum of learning algorithms, from supervised fine-tuning to reinforcement learning such as PPO and GRPO, and the training of reasoners and verifiers. We also examine key designs of agentic workflows, from established patterns like generator-evaluator and LLM debate to recent innovations. ...

Large language models have achieved strong reasoning capabilities, though often at the cost of massive parameter counts and expensive inference. In this work, we explore a different direction: adaptive reasoning depth in compact language models. We present CosmicFish-HRM, a compact language model built around a Hierarchical Reasoning Module (HRM) that dynamically allocates computational effort during inference. Instead of applying fixed computation to every input, the model iterates through high-level and low-level reasoning cycles and learns when to halt based on input complexity. CosmicFish-HRM combines this adaptive reasoning core with modern transformer components including Grouped Query Attention, RoPE, and SwiGLU activations. While the additional reasoning infrastructure introduces overhead at small scale, we hypothesize that this tradeoff becomes increasingly favorable as model size grows and the relative cost of the HRM core diminishes. Our results show that the model learns non-uniform reasoning behavior, allocating different numbers of reasoning steps across tasks and inputs. These findings suggest that adaptive reasoning depth may offer a promising alternative to relying solely on parameter scale for reasoning capability.

This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes our probabilistic type theory from quantum type theory, namely the bijective correspondence between predicates and side-effect free actions (called instrument, or assert, maps). The paper shows how suitable computation rules can be derived from this predicate-action correspondence, and uses these rules for calculating conditional probabilities in two well-known examples of Bayesian reasoning in (graphical) models. Our type theory may thus form the basis for a mechanisation of Bayesian inference.

Large reasoning models (LRMs) have recently achieved significant progress in complex reasoning tasks, aided by reinforcement learning with verifiable rewards. However, LRMs often suffer from overthinking, expending excessive computation on simple problems and reducing efficiency. Existing efficient reasoning methods typically require accurate task assessment to preset token budgets or select reasoning modes, which limits their flexibility and reliability. In this work, we revisit the essence of overthinking and identify that encouraging effective steps while penalizing ineffective ones is key to its solution. To this end, we propose a novel rule-based verifiable stepwise reward mechanism (VSRM), which assigns rewards based on the performance of intermediate states in the reasoning trajectory. This approach is intuitive and naturally fits the step-by-step nature of reasoning tasks. We conduct extensive experiments on standard mathematical reasoning benchmarks, including AIME24 and AIME25, by integrating VSRM with PPO and Reinforce++. Results show that our method achieves substantial output length reduction while maintaining original reasoning performance, striking an optimal balance between efficiency and accuracy. Further analysis of overthinking frequency and pass@k score before and after training demonstrates that our approach in deed effectively suppresses ineffective steps and encourages effective reasoning, fundamentally alleviating the overthinking problem. All code will be released upon acceptance.

Mathematical reasoning models are widely deployed in education, automated tutoring, and decision support systems despite exhibiting fundamental computational instabilities. We demonstrate that state-of-the-art models (Qwen2.5-Math-7B) achieve 61% accuracy through a mixture of reliable and unreliable reasoning pathways: 18.4% of correct predictions employ stable, faithful reasoning while 81.6% emerge through computationally inconsistent pathways. Additionally, 8.8% of all predictions are silent failures -- confident yet incorrect outputs. Through comprehensive analysis using novel faithfulness metrics, we reveal: (1) reasoning quality shows weak negative correlation with correctness (r=-0.21, p=0.002), reflecting a binary classification threshold artifact rather than a monotonic inverse relationship; (2) scaling from 1.5B to 7B parameters (4.7x increase) provides zero accuracy benefit on our evaluated subset (6% of GSM8K), requiring validation on the complete benchmark; and (3) latent reasoning employs diverse computational strategies, with ~20% sharing CoT-like patterns. These findings highlight that benchmark accuracy can mask computational unreliability, demanding evaluation reforms measuring stability beyond single-sample metrics.

Reasoning lies at the heart of intelligence, shaping the ability to make decisions, draw conclusions, and generalize across domains. In artificial intelligence, as systems increasingly operate in open, uncertain, and multimodal environments, reasoning becomes essential for enabling robust and adaptive behavior. Large Multimodal Reasoning Models (LMRMs) have emerged as a promising paradigm, integrating modalities such as text, images, audio, and video to support complex reasoning capabilities and aiming to achieve comprehensive perception, precise understanding, and deep reasoning. As research advances, multimodal reasoning has rapidly evolved from modular, perception-driven pipelines to unified, language-centric frameworks that offer more coherent cross-modal understanding. While instruction tuning and reinforcement learning have improved model reasoning, significant challenges remain in omni-modal generalization, reasoning depth, and agentic behavior. To address these issues, we present a comprehensive and structured survey of multimodal reasoning research, organized around a four-stage developmental roadmap that reflects the field's shifting design philosophies and emerging capabilities. First, we review early efforts based on task-specific modules, where reasoning was implicitly embedded across stages of representation, alignment, and fusion. Next, we examine recent approaches that unify reasoning into multimodal LLMs, with advances such as Multimodal Chain-of-Thought (MCoT) and multimodal reinforcement learning enabling richer and more structured reasoning chains. Finally, drawing on empirical insights from challenging benchmarks and experimental cases of OpenAI O3 and O4-mini, we discuss the conceptual direction of native large multimodal reasoning models (N-LMRMs), which aim to support scalable, agentic, and adaptive reasoning and planning in complex, real-world environments.

Instruction-following is essential for aligning large language models (LLMs) with user intent. While recent reasoning-oriented models exhibit impressive performance on complex mathematical problems, their ability to adhere to natural language instructions remains underexplored. In this work, we introduce MathIF, a dedicated benchmark for evaluating instruction-following in mathematical reasoning tasks. Our empirical analysis reveals a consistent tension between scaling up reasoning capacity and maintaining controllability, as models that reason more effectively often struggle to comply with user directives. We find that models tuned on distilled long chains-of-thought or trained with reasoning-oriented reinforcement learning often degrade in instruction adherence, especially when generation length increases. Furthermore, we show that even simple interventions can partially recover obedience, though at the cost of reasoning performance. These findings highlight a fundamental tension in current LLM training paradigms and motivate the need for more instruction-aware reasoning models. We release the code and data at https://github.com/TingchenFu/MathIF.

Large Language Models (LLMs) have made significant strides in reasoning tasks through methods like chain-of-thought (CoT) reasoning. However, they often fall short in tasks requiring precise computations. Tool-Integrated Reasoning (TIR) has emerged as a solution by incorporating external tools into the reasoning process. Nevertheless, the generalization of TIR in improving the reasoning ability of LLM is still unclear. Additionally, whether TIR has improved the model's reasoning behavior and helped the model think remains to be studied. We introduce ReasonZoo, a comprehensive benchmark encompassing nine diverse reasoning categories, to evaluate the effectiveness of TIR across various domains. Additionally, we propose two novel metrics, Performance-Aware Cost (PAC) and Area Under the Performance-Cost Curve (AUC-PCC), to assess reasoning efficiency. Our empirical evaluation demonstrates that TIR-enabled models consistently outperform their non-TIR counterparts in both mathematical and non-mathematical tasks. Furthermore, TIR enhances reasoning efficiency, as evidenced by improved PAC and AUC-PCC, indicating reduced overthinking and more streamlined reasoning. These findings underscore the domain-general benefits of TIR and its potential to advance LLM capabilities in complex reasoning tasks.

Instruction-driven image editing with unified multimodal generative models has advanced rapidly, yet their underlying visual reasoning remains limited, leading to suboptimal performance on reasoning-centric edits. Reinforcement learning (RL) has been investigated for improving the quality of image editing, but it faces three key challenges: (1) limited reasoning exploration confined to denoising stochasticity, (2) biased reward fusion, and (3) unstable VLM-based instruction rewards. In this work, we propose ThinkRL-Edit, a reasoning-centric RL framework that decouples visual reasoning from image synthesis and expands reasoning exploration beyond denoising. To the end, we introduce Chain-of-Thought (CoT)-based reasoning sampling with planning and reflection stages prior to generation in online sampling, compelling the model to explore multiple semantic hypotheses and validate their plausibility before committing to a visual outcome. To avoid the failures of weighted aggregation, we propose an unbiased chain preference grouping strategy across multiple reward dimensions. Moreover, we replace interval-based VLM scores with a binary checklist, yielding more precise, lower-variance, and interpretable rewards for complex reasoning. Experiments show our method significantly outperforms prior work on reasoning-centric image editing, producing instruction-faithful, visually coherent, and semantically grounded edits.

Chain of thought reasoning has demonstrated remarkable success in large language models, yet its adaptation to vision-language reasoning remains an open challenge with unclear best practices. Existing attempts typically employ reasoning chains at a coarse-grained level, which struggles to perform fine-grained structured reasoning and, more importantly, are difficult to evaluate the reward and quality of intermediate reasoning. In this work, we delve into chain of step reasoning for vision-language models, enabling assessing reasoning step quality accurately and leading to effective reinforcement learning and inference-time scaling with fine-grained rewards. We present a simple, effective, and fully transparent framework, including the step-level reasoning data, process reward model (PRM), and reinforcement learning training. With the proposed approaches, our models set strong baselines with consistent improvements on challenging vision-language benchmarks. More importantly, we conduct a thorough empirical analysis and ablation study, unveiling the impact of each component and several intriguing properties of inference-time scaling. We believe this paper serves as a baseline for vision-language models and offers insights into more complex multimodal reasoning. Our dataset, PRM, and code will be available at https://github.com/baaivision/CoS.

Large Language Models (LLMs) are highly proficient in language-based tasks. Their language capabilities have positioned them at the forefront of the future AGI (Artificial General Intelligence) race. However, on closer inspection, Valmeekam et al. (2024); Zecevic et al. (2023); Wu et al. (2024) highlight a significant gap between their language proficiency and reasoning abilities. Reasoning in LLMs and Vision Language Models (VLMs) aims to bridge this gap by enabling these models to think and re-evaluate their actions and responses. Reasoning is an essential capability for complex problem-solving and a necessary step toward establishing trust in Artificial Intelligence (AI). This will make AI suitable for deployment in sensitive domains, such as healthcare, banking, law, defense, security etc. In recent times, with the advent of powerful reasoning models like OpenAI O1 and DeepSeek R1, reasoning endowment has become a critical research topic in LLMs. In this paper, we provide a detailed overview and comparison of existing reasoning techniques and present a systematic survey of reasoning-imbued language models. We also study current challenges and present our findings.

Large Language Models (LLMs) have demonstrated remarkable capabilities in complex tasks. Recent advancements in Large Reasoning Models (LRMs), such as OpenAI o1 and DeepSeek-R1, have further improved performance in System-2 reasoning domains like mathematics and programming by harnessing supervised fine-tuning (SFT) and reinforcement learning (RL) techniques to enhance the Chain-of-Thought (CoT) reasoning. However, while longer CoT reasoning sequences improve performance, they also introduce significant computational overhead due to verbose and redundant outputs, known as the "overthinking phenomenon". In this paper, we provide the first structured survey to systematically investigate and explore the current progress toward achieving efficient reasoning in LLMs. Overall, relying on the inherent mechanism of LLMs, we categorize existing works into several key directions: (1) model-based efficient reasoning, which considers optimizing full-length reasoning models into more concise reasoning models or directly training efficient reasoning models; (2) reasoning output-based efficient reasoning, which aims to dynamically reduce reasoning steps and length during inference; (3) input prompts-based efficient reasoning, which seeks to enhance reasoning efficiency based on input prompt properties such as difficulty or length control. Additionally, we introduce the use of efficient data for training reasoning models, explore the reasoning capabilities of small language models, and discuss evaluation methods and benchmarking.

Large reasoning models (LRMs) exhibit diverse high-level reasoning patterns (e.g., direct solution, reflection-and-verification, and exploring multiple solutions), yet prevailing training recipes implicitly bias models toward a limited set of dominant patterns. Through a systematic analysis, we identify substantial accuracy variance across these patterns on mathematics and science benchmarks, revealing that a model's default reasoning pattern is often sub-optimal for a given problem. To address this, we introduce Group Pattern Selection Optimization (GPSO), a reinforcement learning framework that extends GRPO by incorporating multi-pattern rollouts, verifier-guided optimal pattern selection per problem, and attention masking during optimization to prevent the leakage of explicit pattern suffixes into the learned policy. By exploring a portfolio of diverse reasoning strategies and optimizing the policy on the most effective ones, GPSO enables the model to internalize the mapping from problem characteristics to optimal reasoning patterns. Extensive experiments demonstrate that GPSO delivers consistent and substantial performance gains across various model backbones and benchmarks, effectively mitigating pattern sub-optimality and fostering more robust, adaptable reasoning. All data and codes are available at https://github.com/wanghanbinpanda/GPSO.

Forecasting has become a natural benchmark for reasoning under uncertainty. Yet existing evaluations of large language models remain limited to judgmental tasks in simple formats, such as binary or multiple-choice questions. In practice, however, forecasting spans a far broader scope. Across domains such as economics, public health, and social demographics, decisions hinge on numerical estimates over continuous quantities, a capability that current benchmarks do not capture. Evaluating such estimates requires a format that makes uncertainty explicit and testable. We propose prediction intervals as a natural and rigorous interface for this purpose. They demand scale awareness, internal consistency across confidence levels, and calibration over a continuum of outcomes, making them a more suitable evaluation format than point estimates for numerical forecasting. To assess this capability, we introduce a new benchmark QuantSightBench, and evaluate frontier models under multiple settings, assessing both empirical coverage and interval sharpness. Our results show that none of the 11 evaluated frontier and open-weight models achieves the 90\% coverage target, with the top performers Gemini 3.1 Pro (79.1\%), Grok 4 (76.4\%), and GPT-5.4 (75.3\%) all falling at least 10 percentage points short. Calibration degrades sharply at extreme magnitudes, revealing systematic overconfidence across all evaluated models.

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

Human problem-solving is never the repetition of a single mindset, by which we mean a distinct mode of cognitive processing. When tackling a specific task, we do not rely on a single mindset; instead, we integrate multiple mindsets within the single solution process. However, existing LLM reasoning methods fall into a common trap: they apply the same fixed mindset across all steps, overlooking that different stages of solving the same problem require fundamentally different mindsets. This single-minded assumption prevents models from reaching the next level of intelligence. To address this limitation, we propose Chain of Mindset (CoM), a training-free agentic framework that enables step-level adaptive mindset orchestration. CoM decomposes reasoning into four functionally heterogeneous mindsets: Spatial, Convergent, Divergent, and Algorithmic. A Meta-Agent dynamically selects the optimal mindset based on the evolving reasoning state, while a bidirectional Context Gate filters cross-module information flow to maintain effectiveness and efficiency. Experiments across six challenging benchmarks spanning mathematics, code generation, scientific QA, and spatial reasoning demonstrate that CoM achieves state-of-the-art performance, outperforming the strongest baseline by 4.96\% and 4.72\% in overall accuracy on Qwen3-VL-32B-Instruct and Gemini-2.0-Flash, while balancing reasoning efficiency. Our code is publicly available at https://github.com/QuantaAlpha/chain-of-mindset{https://github.com/QuantaAlpha/chain-of-mindset}.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks in a stepwise manner. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (2) conditions for convergence to an optimal reasoning policy; (3) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps; and (4) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement. This framework aims to bridge empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Long-form chain-of-thought reasoning has become a cornerstone of advanced reasoning in large language models. While recent verification-refinement frameworks have enabled proprietary models to solve Olympiad-level problems, their effectiveness hinges on strong, reliable verification and correction capabilities, which remain fragile in open-weight, smaller-scale models. This work demonstrates that even with weak verification and refinement capabilities on hard tasks, the reasoning limits of such models can be substantially extended through a probabilistic paradigm we call Deep Self-Evolving Reasoning (DSER). We conceptualize iterative reasoning as a Markov chain, where each step represents a stochastic transition in the solution space. The key insight is that convergence to a correct solution is guaranteed as long as the probability of improvement marginally exceeds that of degradation. By running multiple long-horizon, self-evolving processes in parallel, DSER amplifies these small positive tendencies, enabling the model to asymptotically approach correct answers. Empirically, we apply DSER to the DeepSeek-R1-0528-Qwen3-8B model. On the challenging AIME 2024-2025 benchmark, DSER solves 5 out of 9 previously unsolvable problems and boosts overall performance, enabling this compact model to surpass the single-turn accuracy of its 600B-parameter teacher through majority voting. Beyond its immediate utility for test-time scaling, the DSER framework serves to diagnose the fundamental limitations of current open-weight reasoners. By clearly delineating their shortcomings in self-verification, refinement, and stability, our findings establish a clear research agenda for developing next-generation models with powerful, intrinsic self-evolving capabilities.

Recent advances in reasoning language models have witnessed a paradigm shift from short to long CoT pattern. Given the substantial computational cost of rollouts in long CoT models, maximizing the utility of fixed training datasets becomes crucial. Our analysis reveals that negative responses contain valuable components such as self-reflection and error-correction steps, yet primary existing methods either completely discard negative samples (RFT) or apply equal penalization across all tokens (RL), failing to leverage these potential learning signals. In light of this, we propose Behavior Constrained Policy Gradient with Negative Sample Augmentation (BCPG-NSA), a fine-grained offline RL framework that encompasses three stages: 1) sample segmentation, 2) consensus-based step correctness assessment combining LLM and PRM judgers, and 3) policy optimization with NSA designed to effectively mine positive steps within negative samples. Experimental results show that BCPG-NSA outperforms baselines on several challenging math/coding reasoning benchmarks using the same training dataset, achieving improved sample efficiency and demonstrating robustness and scalability when extended to multiple iterations.

Large reasoning models exhibit remarkable reasoning capabilities via long, elaborate reasoning trajectories. Supervised fine-tuning on such reasoning traces, also known as distillation, can be a cost-effective way to boost reasoning capabilities of student models. However, empirical observations reveal that these reasoning trajectories are often suboptimal, switching excessively between different lines of thought, resulting in under-thinking, over-thinking, and even degenerate responses. We introduce Retro-Search, an MCTS-inspired search algorithm, for distilling higher quality reasoning paths from large reasoning models. Retro-Search retrospectively revises reasoning paths to discover better, yet shorter traces, which can then lead to student models with enhanced reasoning capabilities with shorter, thus faster inference. Our approach can enable two use cases: self-improvement, where models are fine-tuned on their own Retro-Search-ed thought traces, and weak-to-strong improvement, where a weaker model revises stronger model's thought traces via Retro-Search. For self-improving, R1-distill-7B, fine-tuned on its own Retro-Search-ed traces, reduces the average reasoning length by 31.2% while improving performance by 7.7% across seven math benchmarks. For weak-to-strong improvement, we retrospectively revise R1-671B's traces from the OpenThoughts dataset using R1-distill-32B as the Retro-Search-er, a model 20x smaller. Qwen2.5-32B, fine-tuned on this refined data, achieves performance comparable to R1-distill-32B, yielding an 11.3% reduction in reasoning length and a 2.4% performance improvement compared to fine-tuning on the original OpenThoughts data. Our work counters recently emergent viewpoints that question the relevance of search algorithms in the era of large reasoning models, by demonstrating that there are still opportunities for algorithmic advancements, even for frontier models.

Recent progress in large language models has led to the emergence of reasoning models, which have shown strong performance on complex tasks through specialized fine-tuning procedures. While these methods reliably improve pass@1 accuracy, prior works have observed that they show a coverage shrinkage behavior, where pass@k degrades relative to the base model. In this paper, we investigate the reasoning shrinkage arise under SFT-based post-training. We hypothesize that this behavior is driven by properties of the fine-tuning data, specifically related to decision points or "forks in the road" scenarios where model faces indecipherable patterns with multiple valid reasoning paths. To test this hypothesis, we design controlled case studies that simulate such decision-point settings, spanning indecipherable nodes in graph branching, and reasoning modes. By tracking post-training dynamics in these settings, we find that the shrinkage phenomenon is tightly correlated with the prevalence of decision-point scenarios in the training data. We also demonstrate that this shrinkage behavior can be partially mitigated through targeted data synthesis design of decision-points, and a more systematic diversity-encouraging decoding mechanism. Our findings identify data-centric factors as a key driver of shrinkage in reasoning models and highlight diversity-aware designs as an effective lever for controlling it.

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilites can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

Existing methods usually leverage a fixed strategy, such as natural language reasoning, code-augmented reasoning, tool-integrated reasoning, or ensemble-based reasoning, to guide Large Language Models (LLMs) to perform mathematical reasoning. Our analysis reveals that the single strategy cannot adapt to problem-specific requirements and thus overlooks the trade-off between effectiveness and efficiency. To address these issues, we propose Planning and Routing through Instance-Specific Modeling (PRISM), a novel framework that decouples mathematical reasoning into two stages: strategy planning and targeted execution. Specifically, we first curate a multi-strategy preference dataset, which we call MathStrat, capturing correctness, process quality, and computational efficiency for each problem--strategy pair. Then, we train a lightweight Strategy Adapter based on the dataset to obtain confidence distributions over the mentioned four reasoning strategies. At inference time, an adaptive routing policy dynamically tailors the reasoning approach based on predictor confidence. It directs the model to use single-strategy execution for high-confidence predictions, dual-strategy verification for competitive scenarios, or comprehensive multi-strategy exploration for uncertain cases. Extensive experiments across five mathematical reasoning benchmarks demonstrate that PRISM consistently outperforms individual strategies and ensemble baselines, achieving improvements ranging from 0.9% to 7.6% across different base models. The adaptive routing approach shows particularly strong benefits for mathematical reasoning tasks across diverse model architectures. Our code is released at https://github.com/reml-group/PRISM.

We present MiroThinker-1.7, a new research agent designed for complex long-horizon reasoning tasks. Building on this foundation, we further introduce MiroThinker-H1, which extends the agent with heavy-duty reasoning capabilities for more reliable multi-step problem solving. In particular, MiroThinker-1.7 improves the reliability of each interaction step through an agentic mid-training stage that emphasizes structured planning, contextual reasoning, and tool interaction. This enables more effective multi-step interaction and sustained reasoning across complex tasks. MiroThinker-H1 further incorporates verification directly into the reasoning process at both local and global levels. Intermediate reasoning decisions can be evaluated and refined during inference, while the overall reasoning trajectory is audited to ensure that final answers are supported by coherent chains of evidence. Across benchmarks covering open-web research, scientific reasoning, and financial analysis, MiroThinker-H1 achieves state-of-the-art performance on deep research tasks while maintaining strong results on specialized domains. We also release MiroThinker-1.7 and MiroThinker-1.7-mini as open-source models, providing competitive research-agent capabilities with significantly improved efficiency.

Recent studies on large language model (LLM) reasoning capabilities have demonstrated promising improvements in model performance by leveraging a lengthy thinking process and additional computational resources during inference, primarily in tasks involving mathematical reasoning (Muennighoff et al., 2025). However, it remains uncertain if longer reasoning chains inherently enhance factual accuracy, particularly beyond mathematical contexts. In this work, we thoroughly examine LLM reasoning within complex open-domain question-answering (QA) scenarios. We initially distill reasoning traces from advanced, large-scale reasoning models (QwQ-32B and DeepSeek-R1-671B), then fine-tune a variety of models ranging from smaller, instruction-tuned variants to larger architectures based on Qwen2.5. To enrich reasoning traces, we introduce factual information from knowledge graphs in the form of paths into our reasoning traces. Our experimental setup includes four baseline approaches and six different instruction-tuned models evaluated across a benchmark of six datasets, encompassing over 22.6K questions. Overall, we carry out 168 experimental runs and analyze approximately 1.7 million reasoning traces. Our findings indicate that, within a single run, smaller reasoning models achieve noticeable improvements in factual accuracy compared to their original instruction-tuned counterparts. Moreover, our analysis demonstrates that adding test-time compute and token budgets factual accuracy consistently improves by 2-8%, further confirming the effectiveness of test-time scaling for enhancing performance and consequently improving reasoning accuracy in open-domain QA tasks. We release all the experimental artifacts for further research.

Large language models (LLMs) have shown impressive capabilities in handling complex tasks through long-chain reasoning. However, the extensive reasoning steps involved can significantly increase computational costs, posing challenges for real-world deployment. Recent efforts have focused on optimizing reasoning efficiency by shortening the Chain-of-Thought (CoT) reasoning processes through various approaches, such as length-aware prompt engineering, supervised fine-tuning on CoT data with variable lengths, and reinforcement learning with length penalties. Although these methods effectively reduce reasoning length, they still necessitate an initial reasoning phase. More recent approaches have attempted to integrate long-chain and short-chain reasoning abilities into a single model, yet they still rely on manual control to toggle between short and long CoT. In this work, we propose a novel approach that autonomously switches between short and long reasoning chains based on problem complexity. Our method begins with supervised fine-tuning of the base model to equip both long-chain and short-chain reasoning abilities. We then employ reinforcement learning to further balance short and long CoT generation while maintaining accuracy through two key strategies: first, integrating reinforcement learning with a long-short adaptive group-wise reward strategy to assess prompt complexity and provide corresponding rewards; second, implementing a logit-based reasoning mode switching loss to optimize the model's initial token choice, thereby guiding the selection of the reasoning type. Evaluations on mathematical datasets demonstrate that our model can dynamically switch between long-chain and short-chain reasoning modes without substantially sacrificing performance. This advancement enhances the practicality of reasoning in large language models for real-world applications.

Scaling test-time compute by iteratively updating a latent state has emerged as a powerful paradigm for reasoning. Yet the internal mechanisms that enable these iterative models to generalize beyond memorized patterns remain unclear. We hypothesize that generalizable reasoning arises from learning task-conditioned attractors: latent dynamical systems whose stable fixed points correspond to valid solutions. We formalize this process through Equilibrium Reasoners (EqR), which enable test-time scaling without external verifiers or task-specific priors. EqR scales internal dynamics along two axes: depth, by running more iterations, and breadth, by aggregating stochastic trajectories from multiple initializations. Empirically, gains from test-time scaling are tightly coupled with stronger convergence toward solution-aligned attractors. This attractor perspective allows neural networks to adaptively allocate test-time compute based on task difficulty. While simple cases converge within 1 to 5 iteration steps, harder cases benefit from massive test-time scaling. By unrolling up to the equivalent of 40,000 layers, scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme. These results suggest that learned attractor landscapes provide a useful mechanistic lens for understanding scalable reasoning in iterative latent models.

Recent scholarship on reasoning in LLMs has supplied evidence of impressive performance and flexible adaptation to machine generated or human feedback. Nonmonotonic reasoning, crucial to human cognition for navigating the real world, remains a challenging, yet understudied task. In this work, we study nonmonotonic reasoning capabilities of seven state-of-the-art LLMs in one abstract and one commonsense reasoning task featuring generics, such as 'Birds fly', and exceptions, 'Penguins don't fly' (see Fig. 1). While LLMs exhibit reasoning patterns in accordance with human nonmonotonic reasoning abilities, they fail to maintain stable beliefs on truth conditions of generics at the addition of supporting examples ('Owls fly') or unrelated information ('Lions have manes'). Our findings highlight pitfalls in attributing human reasoning behaviours to LLMs, as well as assessing general capabilities, while consistent reasoning remains elusive.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently strengthened LLM reasoning, but its focus on final answer correctness leaves a critical gap: it does not ensure the robustness of the reasoning process itself. We adopt a simple philosophical view, robust reasoning should remain useful beyond the mind that produced it, and treat reasoning as a form of meaning transfer that must survive truncation, reinterpretation, and continuation. Building on this principle, we introduce Reinforcement Learning with Transferable Reward (RLTR), which operationalizes robustness via transfer reward that tests whether a partial reasoning prefix from one model can guide a separate model to the correct answer. This encourages LLMs to produce reasoning that is stable, interpretable, and genuinely generalizable. Our approach improves sampling consistency while improving final answer accuracy, and it reaches comparable performance in substantially fewer training steps. For example, on MATH500, RLTR achieves a +3.6%p gain in Maj@64 compared to RLVR and matches RLVR's average accuracy with roughly 2.5x fewer training steps, providing both more reliable reasoning and significantly more sample efficient.

Large language models often require costly optimization, such as reinforcement learning, to master complex reasoning tasks. This work demonstrates that reasoning ability, once learned, can be extracted and transferred between models as a compact task vector. We source two publicly available, identically initialized Qwen2.5 models, one fine-tuned with supervised fine-tuning (SFT) and the other with group relative policy optimization (GRPO) on the same dataset. From these, we extract a reasoning vector: v_{reason} = theta_{GRPO} - theta_{SFT}. We hypothesize that this vector captures the reasoning capability instilled by reinforcement learning while factoring out shared knowledge from the SFT process. When added to compatible instruction-tuned models through simple arithmetic, this vector consistently improves performance across diverse reasoning benchmarks: GSM8K (+4.9%), HumanEval (+4.3%), SciQ (+1.7%), and BigBenchHard (+12.3% for the 1.5B model). The performance improvements persist under adversarial conditions. Conversely, subtracting the vector causes significant performance degradation (-11.8% on GSM8K), demonstrating the vector's strong contribution to the model's reasoning abilities. This work shows how reasoning capabilities, typically developed through expensive training, can be extracted from existing open-source models and reused through simple tensor arithmetic, offering a practical way to enhance models by recycling prior computational investments.

Large Reasoning Models (LRMs) excel at complex reasoning but are traditionally evaluated in static, "frozen world" settings: model responses are assumed to be instantaneous, and the context of a request is presumed to be immutable over the duration of the response. While generally true for short-term tasks, the "frozen world" assumption breaks down in modern reasoning tasks such as assistive programming, where models may take hours to think through problems and code may change dramatically from the time the model starts thinking to the model's final output. In this work, we challenge the frozen world assumption and evaluate LRM robustness under two realistic dynamic scenarios: interruptions, which test the quality of the model's partial outputs on a limited budget, and dynamic context, which tests model adaptation to in-flight changes. Across mathematics and programming benchmarks that require long-form reasoning, static evaluations consistently overestimate robustness: even state-of-the-art LRMs, which achieve high accuracy in static settings, can fail unpredictably when interrupted or exposed to changing context, with performance dropping by up to 60% when updates are introduced late in the reasoning process. Our analysis further reveals several novel failure modes, including reasoning leakage, where models fold the reasoning into their final answer when interrupted; panic, where under time pressure models abandon reasoning entirely and return incorrect answers; and self-doubt, where performance degrades while incorporating updated information.

As AI systems are being integrated more rapidly into diverse and complex real-world environments, the ability to perform holistic reasoning over an implicit query and an image to localize a target is becoming increasingly important. However, recent reasoning segmentation methods fail to sufficiently elicit the visual reasoning capabilities of the base mode. In this work, we present Segment Anything Reasoner (StAR), a comprehensive framework that refines the design space from multiple perspectives-including parameter-tuning scheme, reward functions, learning strategies and answer format-and achieves substantial improvements over recent baselines. In addition, for the first time, we successfully introduce parallel test-time scaling to the segmentation task, pushing the performance boundary even further. To extend the scope and depth of reasoning covered by existing benchmark, we also construct the ReasonSeg-X, which compactly defines reasoning types and includes samples that require deeper reasoning. Leveraging this dataset, we train StAR with a rollout-expanded selective-tuning approach to activate the base model's latent reasoning capabilities, and establish a rigorous benchmark for systematic, fine-grained evaluation of advanced methods. With only 5k training samples, StAR achieves significant gains over its base counterparts across extensive benchmarks, demonstrating that our method effectively brings dormant reasoning competence to the surface.

Recent advances in reinforcement learning (RL) have led to substantial improvements in the mathematical reasoning abilities of LLMs, as measured by standard benchmarks. Yet these gains often persist even when models are trained with flawed signals, such as random or inverted rewards. This raises a fundamental question: do such improvements reflect genuine reasoning, or are they merely artifacts of overfitting to benchmark-specific patterns? To answer this question, we adopt an evaluation-centric perspective and highlight two critical shortcomings in existing protocols. First, benchmark contamination arises because test problems are publicly available, thereby increasing the risk of data leakage. Second, evaluation fragility results from reliance on single-instance assessments, which are sensitive to stochastic outputs and fail to capture reasoning consistency. These limitations suggest the need for a new evaluation paradigm that can probe reasoning ability beyond memorization and one-off success. As response, we propose VAR-MATH, a symbolic evaluation framework that converts fixed numerical problems into parameterized templates and requires models to solve multiple instantiations of each. This design enforces consistency across structurally equivalent variants, mitigates contamination, and enhances robustness through bootstrapped metrics. We apply VAR-MATH to transform three popular benchmarks, AMC23, AIME24, and AIME25, into their symbolic counterparts, VAR-AMC23, VAR-AIME24, and VAR-AIME25. Experimental results show substantial performance drops for RL-trained models on these variabilized benchmarks, especially for smaller models, with average declines of 47.9\% on AMC23, 58.8\% on AIME24, and 72.9\% on AIME25. These findings indicate that some existing RL methods rely on superficial heuristics and fail to generalize beyond specific numerical forms.

Chain-of-thought (CoT) reasoning enables large language models (LLMs) to break down complex problems into interpretable intermediate steps, significantly enhancing model transparency and performance in reasoning tasks. However, conventional CoT methods rely on heuristic sampling without structured modeling of reasoning transitions, constraining their ability to systematically explore and discover diverse and effective reasoning trajectories. In this work, we introduce CTRLS, a framework that formulates CoT reasoning as a Markov decision process (MDP) with latent state transitions, enabling principled and state-aware exploration via distributional reinforcement learning. By modelling reasoning actions as explicit probability distributions in latent space, our approach explicitly models epistemic uncertainty, facilitating robust exploration of the reasoning space. As part of our framework, we introduce an on-policy reinforcement learning strategy incorporating epsilon-greedy exploration and entropy-based regularization to iteratively refine latent state transitions without requiring additional fine-tuning of the underlying LLM. Theoretical analyses provide evidence lower bounds (ELBO), theoretically grounding our transition-aware modeling of latent reasoning dynamics. Further experiments demonstrate improvements in reasoning accuracy, diversity, and exploration efficiency across benchmark reasoning tasks.

AI-generated content has evolved from monolithic models to modular workflows, particularly on platforms like ComfyUI, enabling customization in creative pipelines. However, crafting effective workflows requires great expertise to orchestrate numerous specialized components, presenting a steep learning curve for users. To address this challenge, we introduce ComfyUI-R1, the first large reasoning model for automated workflow generation. Starting with our curated dataset of 4K workflows, we construct long chain-of-thought (CoT) reasoning data, including node selection, workflow planning, and code-level workflow representation. ComfyUI-R1 is trained through a two-stage framework: (1) CoT fine-tuning for cold start, adapting models to the ComfyUI domain; (2) reinforcement learning for incentivizing reasoning capability, guided by a fine-grained rule-metric hybrid reward, ensuring format validity, structural integrity, and node-level fidelity. Experiments show that our 7B-parameter model achieves a 97\% format validity rate, along with high pass rate, node-level and graph-level F1 scores, significantly surpassing prior state-of-the-art methods that employ leading closed-source models such as GPT-4o and Claude series. Further analysis highlights the critical role of the reasoning process and the advantage of transforming workflows into code. Qualitative comparison reveals our strength in synthesizing intricate workflows with diverse nodes, underscoring the potential of long CoT reasoning in AI art creation.

Large reasoning models (LRMs) are typically trained using reinforcement learning with verifiable reward (RLVR) to enhance their reasoning abilities. In this paradigm, policies are updated using both positive and negative self-generated rollouts, which correspond to distinct sample polarities. In this paper, we provide a systematic investigation into how these sample polarities affect RLVR training dynamics and behaviors. We find that positive samples sharpen existing correct reasoning patterns, while negative samples encourage exploration of new reasoning paths. We further explore how adjusting the advantage values of positive and negative samples at both the sample level and the token level affects RLVR training. Based on these insights, we propose an Adaptive and Asymmetric token-level Advantage shaping method for Policy Optimization, namely A3PO, that more precisely allocates advantage signals to key tokens across different polarities. Experiments across five reasoning benchmarks demonstrate the effectiveness of our approach.

While Large Language Models (LLMs) show remarkable capabilities, their unreliability remains a critical barrier to deployment in high-stakes domains. This survey charts a functional evolution in addressing this challenge: the evolution of uncertainty from a passive diagnostic metric to an active control signal guiding real-time model behavior. We demonstrate how uncertainty is leveraged as an active control signal across three frontiers: in advanced reasoning to optimize computation and trigger self-correction; in autonomous agents to govern metacognitive decisions about tool use and information seeking; and in reinforcement learning to mitigate reward hacking and enable self-improvement via intrinsic rewards. By grounding these advancements in emerging theoretical frameworks like Bayesian methods and Conformal Prediction, we provide a unified perspective on this transformative trend. This survey provides a comprehensive overview, critical analysis, and practical design patterns, arguing that mastering the new trend of uncertainty is essential for building the next generation of scalable, reliable, and trustworthy AI.

Large Language Reasoning Models have demonstrated remarkable success on static tasks, yet their application to multi-round agentic planning in interactive environments faces two fundamental challenges. First, the intractable credit assignment problem renders conventional reinforcement learning ineffective in sparse-reward settings. Second, the computational overhead of verbose, step-by-step reasoning histories is prohibitive. To address these challenges, we propose BPO, a three-stage framework (bootstrapping, extrapolation, and refinement) that establishes a self-improving data flywheel to develop robust reasoning models for long-horizon, sparse-reward environments. Our framework first bootstraps efficient reasoning using the proposed planning quaternions with long-short chain-of-thought fusion. It then extrapolates to out-of-distribution tasks through complexity-stratified curriculum learning. Finally, the model iteratively refines itself by learning exclusively on experiences selected via reward-gated rejection sampling. Experiments on ALFWorld, ScienceWorld, and WebShop demonstrate that our approach achieves state-of-the-art with significant token efficiency, providing a new recipe for reasoning models in agentic planning.

Video reasoning, the task of enabling machines to infer from dynamic visual content through multi-step logic, is crucial for advanced AI. While the Chain-of-Thought (CoT) mechanism has enhanced reasoning in text-based tasks, its application to video understanding remains underexplored. This paper presents a systematic analysis revealing that CoT often degrades performance in video reasoning, generating verbose but misleading internal monologues, and leading to hallucinated visual details and overridden correct intuitions - a phenomenon we term "visual thinking drift". We explain this drift through a Bayesian lens, positing that CoT traces often diverge from actual visual evidence, instead amplifying internal biases or language priors, causing models to storytell rather than engage in grounded reasoning. To counteract this, we introduce Visual Evidence Reward (VER), a novel reinforcement learning framework that explicitly rewards the generation of reasoning traces that are verifiably grounded in visual evidence. Comprehensive evaluation across 10 diverse video understanding benchmarks demonstrates that our Video-VER consistently achieves top performance. Our work sheds light on the distinct challenges of video-centric reasoning and encourages the development of AI that robustly grounds its inferences in visual evidence - for large multimodal models that not only "think before answering", but also "see while thinking".

Actual causality (AC), a fundamental aspect of causal reasoning (CR), is responsible for attribution and responsibility assignment in real-world scenarios. However, existing LLM-based methods lack grounding in formal AC theory, resulting in limited interpretability. Therefore, we propose AC-Reason, a semi-formal reasoning framework that identifies causally relevant events within an AC scenario, infers the values of their formal causal factors (e.g., sufficiency, necessity, and normality), and answers AC queries via a theory-guided algorithm with explanations. While AC-Reason does not explicitly construct a causal graph, it operates over variables in the underlying causal structure to support principled reasoning. To enable comprehensive evaluation, we introduce AC-Bench, a new benchmark built upon and substantially extending Big-Bench Hard Causal Judgment (BBH-CJ). AC-Bench comprises ~1K carefully annotated samples, each with detailed reasoning steps and focuses solely on actual causation. The case study shows that synthesized samples in AC-Bench present greater challenges for LLMs. Extensive experiments on BBH-CJ and AC-Bench show that AC-Reason consistently improves LLM performance over baselines. On BBH-CJ, all tested LLMs surpass the average human rater accuracy of 69.60%, with GPT-4 + AC-Reason achieving 75.04%. On AC-Bench, GPT-4 + AC-Reason again achieves the highest accuracy of 71.82%. AC-Bench further enables fine-grained analysis of reasoning faithfulness, revealing that only Qwen-2.5-72B-Instruct, Claude-3.5-Sonnet, and GPT-4o exhibit faithful reasoning, whereas GPT-4 tends to exploit shortcuts. Finally, our ablation study proves that integrating AC theory into LLMs is highly effective, with the proposed algorithm contributing the most significant performance gains.

Large reasoning models improve with more test-time computation, but often overthink, producing unnecessarily long chains-of-thought that raise cost without improving accuracy. Prior reinforcement learning approaches typically rely on a single outcome reward with trajectory-level length penalties, which cannot distinguish essential from redundant reasoning steps and therefore yield blunt compression. Although recent work incorporates step-level signals, such as offline pruning, supervised data construction, or verifier-based intermediate rewards, reasoning length is rarely treated as an explicit step-level optimization objective during RL. We propose Step-wise Adaptive Penalization (SWAP), a fine-grained framework that allocates length reduction across steps based on intrinsic contribution. We estimate step importance from the model's on-policy log-probability improvement toward the correct answer, then treat excess length as a penalty mass redistributed to penalize low-importance steps more heavily while preserving high-importance reasoning. We optimize with a unified outcome-process advantage within group-relative policy optimization. Extensive experiments demonstrate that SWAP reduces reasoning length by 64.3% on average while improving accuracy by 5.7% relative to the base model.

Large language models (LLMs) now exhibit strong multi-step reasoning abilities, but existing inference-time scaling methods remain computationally expensive, often relying on extensive sampling or external evaluators. We propose a principled strategy that frames reasoning as uncertainty minimisation and operates at the level of individual thoughts rather than tokens. Our method selects, at each reasoning step, the continuation that maximizes the model's self-certainty, a metric computed from its internal predictive distribution. This approach achieves significant improvement with a small number of samples, relies exclusively on model-internal signals, and applies to open-ended questions as opposed to methods like majority voting. Experiments on MATH500 and GSM8K across multiple model sizes demonstrate that thought-level self-certainty maximization consistently outperforms greedy decoding and matches or exceeds self-consistency under comparable token budgets. Cross-linguistic evaluations further indicate that the method transfers robustly beyond high-resource languages. Furthermore, analysis of self-certainty dynamics reveals that correct reasoning trajectories converge early to stable paths, suggesting that early decisions, likely associated with the planning of the reasoning process, are predictive of final accuracy. Building on this result, we show that self-certainty maximisation applied to the early steps can explain most of the performance gain and provide a simple yet efficient inference-time scaling method.

Advanced reasoning in large language models has achieved remarkable performance on challenging tasks, but the prevailing long-context reasoning paradigm faces critical limitations: quadratic computational scaling with sequence length, reasoning constrained by maximum context boundaries, and performance degradation beyond pre-training context windows. Existing approaches primarily compress reasoning chains without addressing the fundamental scaling problem. To overcome these challenges, we introduce InftyThink, a paradigm that transforms monolithic reasoning into an iterative process with intermediate summarization. By interleaving short reasoning segments with concise progress summaries, our approach enables unbounded reasoning depth while maintaining bounded computational costs. This creates a characteristic sawtooth memory pattern that significantly reduces computational complexity compared to traditional approaches. Furthermore, we develop a methodology for reconstructing long-context reasoning datasets into our iterative format, transforming OpenR1-Math into 333K training instances. Experiments across multiple model architectures demonstrate that our approach reduces computational costs while improving performance, with Qwen2.5-Math-7B showing 3-13% improvements across MATH500, AIME24, and GPQA_diamond benchmarks. Our work challenges the assumed trade-off between reasoning depth and computational efficiency, providing a more scalable approach to complex reasoning without architectural modifications.